# Logic questions

Sorry, the template didn't really work for those questions.

1.)
Which of these sentences are propositions? What are their truth values?
a)Boston is the capital of Massachusetts. -> Proposition, but what do they mean by truth values? F and T? Then it would be T.

b) Miami is the capital of Florida. -> proposition. Truth value F?

13. Determine if these bi-conditionals are true or false

a) If 1+1=2, then 2+2=5.

b) If 1+1=3, then 2+2=4.

c) If 1+1=3, then 2+2=5

d) If monkeys can fly, then 1+1=3

Those are all FALSE, right??

Thanks!

Mark44
Mentor
Sorry, the template didn't really work for those questions.

1.)
Which of these sentences are propositions? What are their truth values?
a)Boston is the capital of Massachusetts. -> Proposition, but what do they mean by truth values? F and T? Then it would be T.

b) Miami is the capital of Florida. -> proposition. Truth value F?

13. Determine if these bi-conditionals are true or false

a) If 1+1=2, then 2+2=5.

b) If 1+1=3, then 2+2=4.

c) If 1+1=3, then 2+2=5

d) If monkeys can fly, then 1+1=3

Those are all FALSE, right??

Thanks!

1a) True
1b) False

For an implication (such as 13 a, b, c, and d), the only situation it is false is when the first statement--the hypothesis--is true and the conclusion--the second statement--is false, so 13a is false.

Thanks! Makes sense.

SammyS
Staff Emeritus
Homework Helper
Gold Member
Thanks! Makes sense.
So, what do you think the truth value is for each of: 13b, 13c, 13d ?

False.

Mark44
Mentor
Thanks! Makes sense.

False.
Read what I said again, because you're not getting it. For an implication p $\Rightarrow$ q (also written as if p then q), where p and q are statements, the only possible way for p $\Rightarrow$ q to be false is when p is true and q is false.