 Next one. Question number two. We will complete JEE main. P implies two implies P equivalent to which of them. Moment equivalent comes, please make truth table, without truth table, do not take any kind of a guest. Okay, so let's do the truth table. Sir, I'm not sure I understood the question though. Like how do you identify the roots of the statements and all that? Or is it rational if and only if? Why is it transcendental number? So let's P double arrow Q. Wait, I will take the snapshot of this and pull it to the right screen. Now the best way to solve such kind of question is you should make a truth table with all of them. Oh. Q implies P. P implies P implies Q. P implies P or Q. P implies P. If and only if. Okay. Don't be scared. Just driven by truth table. True to. Let's feel very slow. Okay. First of all, tell me what about this? Q implies Q. Is this true? Yeah. True. Correct? Now P is true and this is true. Husband getting a promotion taking his wife. Good husband? Yeah, yes sir. This can also be said to be true. Yeah. What about this? This is true, this is true. Yeah, everything is true in this thing. True, true, true, everything is true. Up till now, we have not been able to distinguish between the options. Yes sir. Basically, if an eye on this thing marks you with which of them. Okay. Hmm. Then true falls. What about this? One second sir. He took her to Singapore. No, he didn't take her to Singapore even though he got a promotion. What about this? That's false. He didn't get a promotion. Still took his wife. He's a bad husband. Wait. Read, read. Oh, correct. Okay, yeah. Yes sir. He didn't get a promotion. Good husband, huh? So true. Good guy, yeah. True, true. Is true? True. Hmm. Now this will be false. True. True falls, what will it be? Getting a promotion, not taking his wife. This will be false. Yes sir. What about this? P or Q will be true. True, true will be true. Correct. Am I going too fast? No sir. Yeah, okay. Yes, I got it. We'll go back. This was clear, right? Yes sir. Now, this is true, this is false. So what should be the answer for this? Are they saying something? Oh sir, I muted myself. True. P implies Q when P is true and Q is false. Nithya already answered it, it's false. Yeah. Now this is true. Now think as if this is the husband's promise and this is the taking of the wife to Singapore. Getting a promise, not taking the wife. Okay, bad. False, correct? Yeah, yes sir. Now do the same thing over here also. What is P or Q? True. Yeah, true. And this is already true, P is already true. Getting a promotion and good husband, correct? Yes sir. The moment you realize that this is not mapping with this, that means this cannot be true. Option A is ruled out. Option A to A. Going forward, I am not going to waste time on this option. This is crap. Yeah. Let's see what else we can scrap. Now this is going to be true and this is going to be false, right? Yes sir. This is also going to be true. Correct now? Yeah. Yeah. This is true, this is going to be false. So this is also going to be false. So this is also going to be scrapped. Yes sir. You don't have to do any further, don't waste your time because that is not going to end up giving you anything. You just have to mark option B and move on. Yes sir. Yeah, got it sir. Does it make sense to you or not? Everybody, it's a question for everybody. So it makes sense, it's just a little slow. It takes a bit of time to write. Yeah, it takes time. Another way is yeah. Third one. Statement one says negation of if and only if p then q is equivalent to, if and only if p then q. Okay. That's false. How do you can do this so fast? Sir, then you try expanding this. You'll get that, that thing P, that double arrow, double, double q. Okay. If this is wrong, then you had it from me. You said first statement is false. Okay. That's false. That's false. That's false. That's false. That's false. That's false. That's false. That's false. That's false. You said first statement is false, right? Yeah. If this is wrong, then see what I do to you. Okay, sir. That means it's going to be false. My statement. No, it may be correct also, but we did not jump so early. Yes, sir. It may be correct also. I'm just kidding you. I will not, I'll do some calculations in my mind also. Let's take true, true. So this is false. Yes, sir. False. Okay. Now what about this? Both, yeah. True false, it has to be false because this is false. Both are true or both are false. Yes, sir. This is true. And this guy will also be true. Okay. Yeah. True. True. True. True. True. True. True. And now see true. True. True. That guy is true. This guy is false. False. And now look here. True false, false. Thank you. False. This is false. False. Now look at this guy and this guy. False false means true. Yeah. Negative. False. Now these two will be false. Thank God. False false. This is true. Okay. Then this and this will be false. False. That'll be true. False false is true. True. Yeah. See, don't jump into a conclusion. So this is a true statement. Yes, they are equivalent. Okay. So statement one is true. True. Now do the statement number true. Okay. Yes, sir. Is that a tautology? Hey, you. Tautology. Tautology. Okay. One second, sir. P. Q. It means whatever you put your answer for this will always be true. Is that the case? Check money. Yes. So let's see. True. True. True. True. No, sir. It's not a tautology. Actually you're correct. So this is true. No. Fine. See, right? See is done. Yeah. Next. If alpha beta the roots of this. This is not a. Yes. This will do. This will do. This seems like a. Same question. Minus omega and minus omega squared. Minus omega squared. Yes. Just put it in. Yes. Okay. I think I've already done. Okay. So we lose six one. Six one six one. Yes, sir. Six one is. Consider the following statement. So one is brilliant. So one is rich. So one is honest. Okay. Which of the following statement represents the negation of the statement. So is brilliant and dishonest if and only if someone is very obvious. Very obvious. See from the options that. What do you think? I'm thinking that it's. Okay sir. Someone is brilliant and dishonest. So total the answer one second. Brilliant is the honest. That and dash. if and only if it is rich. So basically this by condition with if and only if it is rich. Rich is q, right? Yeah. This is your answer. Yeah. Which option? Not this one. Not this one. Yeah, this one. See. Oh, sir, why can't we solve it like p of thing that dash r maps to double maps to q. Conjunction not r. Sir. Now it has conjunction. Conjunction. Yeah, this guy's conjunction. See here, someone is brilliant and dishonest. So this is one statement which is connected with if and only if someone is rich. Correct? Yeah. So if someone is rich, if and only if symbol. Hmm. Someone is brilliant is p. P and dash r. Okay. Conjunction. Dishonest is negation of r. The whole thing's negation you want. This is the answer. Oh, yeah. Yes, sir. The negation of this. Then I will open a school. I told you that negation of p implies q is same as saying p and not q. And not q. And I will not open a school. Open a school. Yeah. Yeah. What type of questions were coming in the past so easy. Very scoring topic, but not leave out any. Sir, the subjective questions were hard and then from 2000 to 2000 like 11 it became damn easy. Now it became harder again. I think 1900s, 1970s now I just seen one question that they were hard and 2000s to 2011 as long as it became damn easy. Then again it started becoming difficult. Oh, is it like that? Yeah. Who gave you that trend analysis? I saw some questions. Okay. Next. Consider statement one and statement one is a falsely statement two is a totality. One is true. I think I made. Sorry, sir. I don't think I was listening right. What's a tautology again? Oh my God. Something which is always true. Policy which is always false. Okay. Outcome of this. If you do a table for this, it should always give you false false false. That seems to one second. That was an honest confession from the red. Just let me know when you're done with the first one. Two is also true. Statement one. Statement one when you're done. First one is true. Both statement one and two are true. Not sure about the explanation. Okay one second bro. I'm still doing the first one. statement one and two are both are true. Yeah. This one I know. According to you, the beat should be the answer, right? Correct explanation. Yes, sir. But once again, I won't, I'm not yet given my verdict on the first statement. Okay. I'm waiting for your verdict. False and false false false false false. Yes, sir. First one is false. I mean it's a fallacy is true. Okay. We'll check. So P and not true. This is false. The FF. This is going to be T. This is going to be F. This is going to be F. Not Q is false. True is false. FFTF. False T. False. Okay. So I'm slightly faster. Then you're taking the conjunction of this. So this will be false. False false false. This is definitely a false. False. This is our true statement. Okay. Yeah. Next one. Total G. So the sad part is only one option gets eliminated in these kind of things. You. Hey, we don't have to do this also. This is a. Contra positive of the same statement. Okay. I didn't see that. So let's do the, let me call this our and this is. This is our itself, right? Yes, sir. Okay. Okay. This will always be a true, right? Yeah. This will also be true. This is false. This will also be false. Yeah. The true, true will always be true. This is a tautology. Yeah. But they are nowhere. So you can see. Absolutely. You're absolutely correct. Two is true, but two is not a correct explanation for one.