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Had some difficulty doing this:

1) if $1+1 = 3$, then $2+2 = 4$ (This should be true)

2) if $1+1 = 3$ then cows can fly

3) if $1+1 = 2$ then God exists

4) if $2+2 = 4$ then $1+2 =3$

I understand that the truth table of a implication A→B is false only when A is true and B is false. How can i prove God exists to be true or false?

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    Correct: so, the answer to 3) must be : it depends... – 2017-02-05

2 Answers 2

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The answer solely depends on your view about the existence of God. However, giving $T$ or $F$ value to such opinion based sentences is meaningless as it doesn't qualify to be in the category of statement.

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Let first statement in each case is P and second Q.

1) P is false and Q is true so statement is true.

2) P is false. When P is false then whatever value of Q. Statement is true in if-then case.

4) P & Q true. So statement is true.

But in case 3, P is true and we don't know the truth value of Q. So two cases.

Case 1-

If Q is true statement 3 true.

Case 2-

If Q is false statement 3 false.