HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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Solution for Prove that the following statement pattern is equivalent : (p ∨ q)  r and (p → r) ∧ (q → r) - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

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Question

Prove that the following statement pattern is equivalent :

(p ∨ q)  r and (p → r) ∧ (q → r)

Solution

 

Truth table given is as follows:

1 2 3 4 5 6 7 8
p q r

`A=p vv q`

`B=p->r`

`C=q->r`

`A->r`

`B ^^ C`

T T T T T T T T
T T F T F F F F
T F T T T T T T
T F F T F T F F
F T T T T T T T
F T F T T F F F
F F T F T T T T
F F F F T T T T

Thus from column 7 and 8 

(p ∨ q)  r ≡(p → r) ∧ (q → r)

 
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APPEARS IN

 2014-2015 (March) (with solutions)
Question 2.1.1 | 3.00 marks

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Solution Prove that the following statement pattern is equivalent : (p ∨ q)  r and (p → r) ∧ (q → r) Concept: Mathematical Logic - Statement Patterns and Logical Equivalence.
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