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

ConceptStatement Patterns and Logical Equivalence

#### 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)

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 2.1.1 | 3 marks

#### Video TutorialsVIEW ALL [1]

Solution for question: Prove that the following statement pattern is equivalent : (p ∨ q)  r and (p → r) ∧ (q → r) concept: null - Statement Patterns and Logical Equivalence. For the courses HSC Arts, HSC Science (General) , HSC Science (Electronics), HSC Science (Computer Science), HSC Commerce, HSC Commerce (Marketing and Salesmanship)
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