Question

Complete each statement so it will result in the truth value F.

If the GCD of 5 and 12 is 1, then _______
-> 12 is even
->12 is less than 5
->5 is less than 12
->5 is prime

The sum of 5 and 12 is 7 if and only if _______
->12 is divisible by 5
-> 12 is greater than 5
-> 5 is even
->the difference between 12 and 5 is -7

Answer 1

We want to create sentences that are false (this means that the truth value is F

False ---> true: then the statement is false

true-----> false: then the statement is false.

For the first option we have:

"If the GCD of 5 and 12 is 1,____"

the left side is true, so the right side must be false:

"If the GCD of 5 and 12 is 1, then 12 is less than 5"

this means that the truth value is false, because the left side is true and the right side false.

For the second sentence we have:

The sum of 5 and 12 is 7 if and only if _______

The left side is false, so the right side must be true, the only true option is 12 is greater than 5, so the sentence is:

"The sum of 5 and 12 is 7 if and only if 12 is greater than 5."