QuestionWhich two conditional statement forms always share the same truth value? A. statement and inverse B. inverse and contrapositive C. converse and contrapositive D. converse and inverse
Studdy Solution
STEP 1
Assumptions1. We are dealing with conditional statements, which are statements of the form "if then Q", denoted as -> Q.
. The inverse of a conditional statement is "if not then not Q", denoted as ~ -> ~Q.
3. The converse of a conditional statement is "if Q then", denoted as Q ->.
4. The contrapositive of a conditional statement is "if not Q then not", denoted as ~Q -> ~.
STEP 2
We need to determine which two forms of a conditional statement always have the same truth value.
STEP 3
The statement and its contrapositive always have the same truth value. This is a fundamental property of logic. So, the contrapositive (~Q -> ~) always has the same truth value as the original statement ( -> Q).
STEP 4
Similarly, the converse (Q ->) and the inverse (~ -> ~Q) always have the same truth value. This is another fundamental property of logic.
STEP 5
Therefore, the two pairs that always have the same truth value are the statement and its contrapositive, and the converse and its inverse.
So, the correct answer is B. inverse and contrapositive, and D. converse and inverse.
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