 Hello, logicians. Now that you've had a brief exposure to conditional and converse statements, we're going to practice those skills to solidify them. I have statement P, two planes are parallel, and statement Q, two planes do not intersect. We are going to turn those two statements into a conditional statement using if, then. So the conditional statement is if two planes are parallel, then two planes do not intersect. Down below in my little truth table, that is a true statement. If two planes are parallel, they do not intersect. So I am going to say that that is true. Now pause the video and you write the converse. So the converse is switched. You write the Q part of the statement first and the P part of the statement second. If two planes do not intersect, then two planes are parallel. And that statement is true. If both the conditional and the converse are true, if both parts of this table are true, then we can write a biconditional and it also will be true. So here comes the biconditional. So the final statement is the biconditional. Notice that it doesn't start with if. It doesn't have a then in it. It has an if and only if in the middle, meaning that the truth value goes both ways just as you will notice that the symbol for if and only if is a double arrow. It goes both ways. Two planes are parallel, if and only if two planes do not intersect. So now we have another set of statements. P, two angles are vertical angles and Q, two angles are congruent. Pause the video and you write the conditional statement before you see how I have written it. Practice writing conditional statements. Pause the video. So the conditional statement is if two angles are vertical angles then two angles are congruent. And the truth value of that is true. It is true. If two angles are vertical then they are also congruent. Now pause the video and write the converse. The converse statement is if two angles are congruent then those two angles are vertical. The truth value of that is false. Just because two angles are congruent doesn't necessarily mean they're vertical. They could be in completely different rooms. They could be in different planes. There's nothing about congruent that says that they have to be vertical. So if either one of these statements is false you cannot write a biconditional. It's just you don't write it. It doesn't have a truth value. It's you skip it. That's how you handle conditional statements and how you create biconditional statements. Now there's a third set, a third pair of statements on your sheet. Do those independently using this information and show your teacher your skills in class tomorrow.