Question

Let P() and Q() be open sentences where the universal set of the variable is T. Which of the following implies that P()→Q() is true for all in the universal set T?

Answer 1

A statement that implies that P()→Q() is true for all x in the universal set T is 'If Q(x) is true for all x in T, then P(x) is true for all x in T.'

Step-by-step explanation:

A statement that implies that P()→Q() is true for all x in the universal set T is:

1. If Q(x) is true for all x in T, then P(x) is true for all x in T.

This statement states that whenever Q(x) is true for all x in T, then P(x) is also true for all x in T. This confirms that P()→Q() is true for every element in T.