Let p be x is cubed and let q be x3 is greater than x Write

Let p be \"x is cubed, \" and let q be \"x^3 is greater than x.\" Write each statement below in words, then state whether the statement is true or false. A. The conditional statement is true or false. B. The converse q rightarrow p C. The inverse ~ p rightarrow ~ q D. The contrapositive ~q rightarrow ~ p

Solution

A. The conditional statement : If P, then Q. - True

If x is cubed, then x³ is greater than x.

B. The converse : If Q, then P. - False

If x³ is greater than x, then x is cubed.

C. The inverse : If not P, then not Q. - False

If x³ is not greater than x, then x is not cubed.

D. The contrapositive : If not Q, then not P. - True

If x is not cubed, then x³ is not greater than x.