Briefly explain how the following tautologies may be used in the method of proof by contradiction: (~p =>(q ∧ ~q)) => p
Briefly explain how the following tautologies may be used in the method of proof by contradiction: (~p =>(q ∧ ~q)) => p
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Briefly explain how the following tautologies may be used in the method of
proof by contradiction: (~p =>(q ∧ ~q)) => p
Expert Solution
Step 1
As per the instruction, we will prove the statement (~p =>(q ∧ ~q)) => p as tautologies by contradiction.
By contradiction, let us assume (~p =>(q ∧ ~q)) is true and p is false.
And now, we will find a contradiction.
So,
1. (~p =>(q ∧ ~q))
2. ~p =>(False) (By Contradiction)
3. ~p is False (By Simplification)
4. p is True (By Negation)
But as per our assumption p is false.
Hence, the assumption that (~p =>(q ∧ ~q)) is true and p is false are incorrect.
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