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GO Classes DPP | GATE CS | Discrete Mathematics| Propositional Logic

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3 3 votes

Consider the implication: "If $\mathrm{a} / \mathrm{b}$ and $\mathrm{b} / \mathrm{c}$ are integers, then $\mathrm{a} / \mathrm{c}$ is an integer." Which of the following is the contrapositive of this statement?

  1. If $\mathrm{a} / \mathrm{c}$ is an integer, then $\mathrm{a} / \mathrm{b}$ and $\mathrm{b} / \mathrm{c}$ are integers.
  2. If $\mathrm{a} / \mathrm{b}$ is not an integer or $\mathrm{b} / \mathrm{c}$ is not an integer, then $\mathrm{a} / \mathrm{c}$ is not an integer.
  3. If $\mathrm{a} / \mathrm{c}$ is not an integer, then $\mathrm{a} / \mathrm{b}$ is not an integer or $\mathrm{b} / \mathrm{c}$ is not an integer.
  4. If $\mathrm{a} / \mathrm{c}$ is not an integer, then $\mathrm{a} / \mathrm{b}$ is not an integer and $\mathrm{b} / \mathrm{c}$ is not an integer.

3 Answers

1 1 vote

Statement : P→Q 

contrapostive statemen : ¬Q→¬P. 

if a/b  and b/c are an integers then a/ c is an integer(given statement) 

contrapostive statement : 

if a/ c is not an integer then  a/ b is not an integer  or b/c is not an integer  

so Option c is correct. 

0 0 votes

In Propositional Logic, the contapositive of a statement is a very important concept.

Definition

If you have a statement:

P→Q 

Its contapositive is:

¬Q→¬P
So ans : C

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