00:01
Okay, so this question is saying, if the antecedent of a conditional statement is false, the conditional statement is true.
00:09
So let's write out what that means.
00:11
A conditional statement is something that looks like this.
00:14
If p, then q.
00:16
And the p, the part in front of the arrow, is our antecedent.
00:22
So we want to know that if p is false, will this statement, if p, then q, be true? true.
00:29
Let's look at our truth table for this just to remind ourselves what it looks like.
00:38
So our values for p and q, our inputs, are just all of the options of true or false there, all the combinations.
00:47
And then our output, if p then q, is saying that if p is true, q is guaranteed to be true for this statement to be true.
00:55
So when p is true and q is true, this statement is true.
00:59
But when p is true and q is false, that means our statement has led us down and it is false.
01:05
The next two are where p is false...