Which of the following sentences is a proposition whose truth value is T? Select one: a. x + 2 = 11 b. x + y = y + x for every pair of real numbers x and y c. Answer this question carefully. d. Manila is in Cagayan.

$a)$

$x + 2 = 11.$

The given statement can neither be true or false. It depends on the value of x. Hence, it is not a proposition.

$b)$

x + y = y + x for every pair of real numbers x and y

This is a proposition whose truth value is $T.$

$c)$

 Answer this question carefully.

Since " Answer this question carefully" is not a statement that can be either true or false, it is not a proposition.

$d)$

Manila is in Cagayan.

This statement is a proposition whose truth value is $F$ .

Therefore, the correct choice is b.