Question

Let A and B be arbitrary but fixed statements. Let S be the statement A→B. Which of the following statements is true?
Select one:
a. If S is true, then the contrapositive of S is true
b. If the negation of S is true, then the negation of the contrapositive of S is false
c. If the inverse of S is true, then the converse of S is false
d. none​

Answer 1

Answer:

answer ia a...............

Answer 2

Answer:

The answer is option a. If S is true, then the contrapositive of S is true.

Explanation:

• Contrapositive involves negating certain logical statements.
• Sometimes the given proposition already contains certain negative statements, and contrapositive is the natural choice.
• The conditional statement is in the form of,
• "If A, then B."
• W can try to proof it directly . If the direct method fails, we can do the contradiction proof. The proof can be done only if the statement is in the form of,
• "If A, then B." (A⇒B)
• Which is equivalent to,
• "If ¬ B then, ¬ A."  (¬ B ⇒ ¬ A )
• The above statement is called the contrapositive of the first.
• Instead of proving that A ⇒ B, you prove directly that ¬B ⇒¬A.

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