in Mathematical Logic
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According to the principle of logic, an implication and it's contrapositive must be

  1. both true or both false
  2. both true
  3. both false
  4. none
     
in Mathematical Logic
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3 Answers

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Best answer
Direct and Contrapositive always have same truth value.
Inverse and Converse always have same truth value.
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Implication and contrapositive both can same values in truth table and at same time they can be either true of false So

option (A) is correct .
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  1. $P\rightarrow Q$ // F
     
  2. $Q\rightarrow P$ //Converse of F
     
  3. $\sim P\rightarrow \sim Q$ // Inverse of F
     
  4. $\sim Q\rightarrow \sim P$ // Contrapositive of F

 

F is actually equivalent to contrapositive of F. So both have the same value. Option A


If you take the converse of F, and apply contraposition to it, you'll find that converse of F is actually equivalent to the inverse of F. They have the same value too.

In other words: 1 is equivalent to 4; 2 is equivalent to 3.

Answer:

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