Question

Is the contrapositive of the following conditional true?

If x ≥ 4, then x > 2.
yes
no

Answer 1

Explanation:

The contrapositive of a conditional statement "if p, then q" is "if not q, then not p." In this case, the given conditional statement is "if x ≥ 4, then x > 2." To find the contrapositive, we negate the original statement. The negation of "x ≥ 4" is "x < 4" and the negation of "x > 2" is "x ≤ 2." Therefore, the contrapositive of the given conditional statement is "if x ≤ 2, then x < 4." Now, let's determine if the contrapositive is true. If x ≤ 2, then x < 4. This statement is true because any value of x that is less than or equal to 2 will also be less than 4. So, the contrapositive of the given conditional statement is true.