 Which of the following is true for any two statements P and Q? This is a symbol for equivalence. This is a symbol. The same that we use for congruency. Okay, Vidyota. Multiple may be correct. So please be careful. Oh, okay. Okay, sir. One second. This is not all of it. By the way, second question is in the middle. Yeah. One sec, sir. One sec. Almost got it. Sir, a contradiction here is what? I understood what contradiction actually means, but what is it in this context? When this output will always fall. Oh, okay. That means policy. Yeah. Oh, okay. So one sec. And right. Yes, sir. This is incomplete. Yes, sir. A and C. Okay. Okay. Let me check about the P option. Yes, sir. This will be true, but this will be true and false will be false. Okay. Next is true false. This will be false. And false into false and truly false. False and truly false. And this will be false. The false and false will be false. And finally you have false, false. So this will be false, but this will be true. So this is a contradiction C is also correct. Yes, sir. So why did you leave out that symbol that they have made? Let it be this symbol. Okay. What about others? One sec, sir. I just now figured out how to do it. Let's discuss. Yes, sir. Substitute options, right? Yes, you can do that only. So let's say true false false and C is true. Q is false and R is true. R is also false. True and true. Yes, sir. And this is and, this is false and false. Which is false. The true and true false. False. Okay. What about others? False and true gives false. No, no, no. P, Q, R. False and false is false again. Oh, yeah. And true and false. True and false is false. So false and false is false. So this is also correct. Next. False and false. So this will be false. Yes, sir. This will be true. And true. False and true. False again. This I don't think. So this will be true and false. False. The moment one is false. Yeah. Here we could have saved time by checking if any one of them is false. Oh yeah. Next. Total. 16th one. Sir, can something be a tautology and contradiction at the same time? No, right? No. Correct. Yes, sir. That's the whole genesis of calling a statement because the dealing with statement. A statement cannot be simultaneously true and false. Yeah. It has to be a tautology because both are same things, right? Yes, sir. So 17 means the right answer. Correct. 18th. In the third option 18, should we assume some sign between there? Oh yeah, they are missing out on the sign. Okay. What is P? P is false, right? P is false. So wherever there's a negation of P, there should be there. So P is false. 6 is the divisor of 12th and this is also true. SCF of this is true. This is also true. Hmm. Which is true? This cannot be true. That can't be true. Huh? Sorry. Yeah, correct, sir. Yes, sir. Nothing, nothing. This is true, intersection, false. So this is really false. This is also true. And this is true or true. True or true is true. That means option D is the right answer. Okay, correct. 19th. I'm sending you, sir. Send. Others. Okay, let's discuss. Here, have you already know the truth table for this? Hmm. What is that? True, true is true. True false is false. False false. False true is true. False false is true, right? Hmm. Just remember this. Okay. What about other way. True. True false true. If I take orange. Yes. The truth. And then two is true. Okay. This. Then. and true will be false. Yes sir. Then true and true. This is not logical. Yes sir. Let us take this one. p and q will be true or okay let me write it like this. True, true or will be true. Now if you have true false for both of them this will be false while this will be true. And then or will be true again which doesn't match with this. Yes sir. Last one. Sorry b1. p or q will be true and this is a tautology. This is also going to be matches. Oh correct correct. This is a tautology right. Yes sir. Didn't see that option earlier. Okay What about this one? Here you are taking the union of true. So true, true is true. False, true is true. False, true is true right. False, true. He didn't take her but he got promotion. If this is true and this is false that means I am taking into account this case. True and this is false correct. Yeah. Then your answer is going to be true correct. This is the other one he didn't get but he took. If this guy is false and this guy is true my answer should be true again but here the answer is false. Yeah. None of these are logically given. Yeah. So can you just check the a1 again? I feel that might be the answer. Okay I will check again. I think it's the whole tab here. I will take this question separately. Okay. So let's have p, q, p implies q, q implies p and then you are saying to check a right. So p implies q or q implies p. So if the truth table of this matches with this that means statement a is correct. Let's check. True, true, false, false, true, false, false. True, true, false, false, true. Sorry true, false, true. Yeah. If you look at Ulta then this will be true, true, false, true. Yeah. Now they are taking their or. So or will be true, true. Okay. True. This is actually a tautology. Okay, sir. I mean this is not matched. Yes, sir. Even if you take their hands will be nice, true, true, false, true. Yeah. It also doesn't match with this. Oh they should have given q equal to implies p and then probably and here and and then it'll be correct. Yeah. But two mistakes didn't make it right this time.