The Gateway to Computer Science Excellence
0 votes
105 views

Determine whether (p ∧ ( p → q )) → q is Tautology , Contradiction or Contingency. 

in Mathematical Logic by Active (3.8k points)
edited by | 105 views

2 Answers

+3 votes
Best answer
p q p → q p ∧ ( p → q ) (p ∧ ( p → q )) → q
0 0 1 0 1
0 1 1 0 1
1 0 0 0 1
1 1 1 1 1

Since , all are 1, hence tautology

by Veteran (50.9k points)
selected by
+2 votes

(p ∧ ( p → q )) → q

≡(p ∧ ( ~ p ∨ q )) → q

≡~(p ∧ ( ~ p ∨ q ))  ∨ q

≡(~p ∨ (  p ∧ ~q ))  ∨ q

≡(~p ∨ p ) ∧ ( ~p ∨ ~q ) ∨ q

≡( ~p ∨ ~q ) ∨ q

≡~p ∨ (~q ∨ q)

≡~p ∨ T

≡T

Hence,(p ∧ ( p → q )) → q is Tautology. 

by Boss (41.2k points)
+2

good one ...accurate procedure ..it tells u know the concept wellyes
 

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,741 questions
57,251 answers
198,056 comments
104,682 users