Given below are two statements: Statement A: "All physicians whose licenses have been revoked are physicians ineligible to practise". Statement B: "All physicians eligible to practise are physicians whose licenses are intail". Which of the following is true with regard to above two statements?

Given below are two statements: Statement A: "All physicians whose licenses have been revoked are physicians ineligible to practise". Statement B: "All physicians eligible to practise are physicians whose licenses are intail". Which of the following is true with regard to above two statements? Correct Answer <span style="">Statement B is contrapositive of the statement A and these two statements are logically equivalent.</span>

In conditional statements, "If p then q" is denoted symbolically by "p q"; p is called the hypothesis, and q is called the conclusion.

Key Points

The contrapositive of a conditional statement of the form "If p then q" is  "If  ~q then  ~p". 

• Symbolically, the contrapositive of p q is ~q~p.
• A conditional statement is logically equivalent to its contrapositive.

​Statement A: "All physicians whose licenses have been revoked are physicians ineligible to practice"

• Let P stand for the statement "All physicians whose licenses  have been revoked"
• Let q stand for the statement  "physicians ineligible to practice"

Statement B: "All physicians eligible to practice are physicians whose licenses are entailed".

• Let ~q stands for "All physicians eligible to practice"
•  Let ~p stands for "physicians whose licenses are entailed" 
• ​This follows logically from our initial statement and, like it, it is evidently true.

​​Thus, Statement B is the contrapositive of statement A and these two statements are logically equivalent. 

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