Question

What is the truth value for the following conditional statement? If the snow is white, then the grass is red.

Answer 1

Assuming snow is actually white, and grass is green, then the statement is false, because
A->B is false whenever A is true and B is false.
But watch out that the statement is true when A is false.

Answer 2

False.

Explanation:

If the snow is white, then the grass is red. We have a conditional of the form

`p\rightarrow q` where

p = the snow is white

q = the grass is red.

Now, the snow is in fact white, then p is true. But, the grass is not red, then q is false. That is, we have

`p\rightarrow q` with p true and q false.

The conditional statement
`p\rightarrow q` is false only if p is true and q is false. Then, the truth value of "If the snow is white, then the grass is red" is false.