GATE CS 2014 Set 3 — Question 11
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Engineering Mathematics → Mathematical Logic → Logical Equivalence
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Question
Consider the following statements:P: Good mobile phones are not cheap
Q: Cheap mobile phones are not goodL: P implies Q
M: Q implies P
N: P is equivalent to QWhich one of the following about L, M, and N is CORRECT?
Q: Cheap mobile phones are not goodL: P implies Q
M: Q implies P
N: P is equivalent to QWhich one of the following about L, M, and N is CORRECT?
Correct answer
(D) L, M and N are TRUE.
Solution
Let denote " is a good mobile phone" and denote " is a cheap mobile phone".Statement P: "Good mobile phones are not cheap" can be written as:
Statement Q: "Cheap mobile phones are not good" can be written as:
The contrapositive of () is , which simplifies to .
Since a statement is logically equivalent to its contrapositive, .Therefore:
Statement Q: "Cheap mobile phones are not good" can be written as:
The contrapositive of () is , which simplifies to .
Since a statement is logically equivalent to its contrapositive, .Therefore:
- L: P implies Q is TRUE (since they are equivalent).
- M: Q implies P is TRUE (since they are equivalent).
- N: P is equivalent to Q is TRUE.
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