Video: Using the Law of Syllogism

Which of the following statements follows logically from statements A and B? A. If Liam misses the bus, then he will be late for work. B. If Liam is late for work, then he will not be paid a bonus. [A] If Liam was not paid a bonus, then he missed the bus. [B] If Liam was not paid a bonus, then he was late for work. [C] If Liam was late for work, then he missed the bus. [D] If Liam misses the bus, then he will not be paid a bonus.

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Video Transcript

Which of the following statements follows logically from statements A and B? A) If Liam misses the bus, then he will be late for work. B) If Liam is late for work, then he will not be paid a bonus.

Then, we have four different conclusions to walk through. But before that I want to remind us about conditional statements. We sometimes use the letter p and q to talk about conditional statements: if p, then q. In statement A, if Liam misses the bus, then he will be late for work — if p, then q. The logic for these statements move in one direction from p to q. We cannot turn them around and say if q, then p. That is not logical. If we try that here, it would say, “If Liam will be late for work, he missed the bus.” But there are other reasons that Liam could be late for work, besides just missing the bus, maybe even the bus was late. We cannot say for certain “If Liam was late, then he missed the bus.” But we can say for certain “If he misses the bus, then he will be late.” That is what our statement is saying.

Next, for statement B, we take the conclusion from statement A, if Liam is late for work and it becomes the if statement. It becomes the conditional. The new conclusion is f, if Liam is late for work, then he will not be paid a bonus. Again, we have to remember that these logic statements move in one direction. We cannot turn them around and expect them to be true. We need to look for a statement that logically flows from the beginning of statement A to the end of statement B.

We can break down each of these options. a) says, “If Liam was not paid a bonus, then he missed the bus.” “If Liam was not paid a bonus” we represent that with the letter f, “then he missed the bus” we represent that with the letter p. This statement is trying to go from f to p and it’s not possible. After that, “If Liam was not paid a bonus,” represented with the variable f “then he was late for work” represented with the variable q: this statement is moving in the wrong direction for conditional statements. And anyway, there could be plenty of other reasons why Liam wasn’t paid a bonus.

The third option “If Liam was late for work,” q “then he missed the bus” p: we’ve already talked about this option, it’s moving the wrong direction. Finally, we have “If Liam misses the bus,” p “then he will not be paid a bonus” f: this statement is logically flowing from our original statements A and B.

We can rightly say, “If Liam misses the bus, then he will not be paid a bonus.”

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