HSC Arts 12th Board ExamMaharashtra State Board
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# Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency. - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptMathematical Logic Truth Value of Statement in Logic

#### Question

Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.

#### Solution

No of rows = 2n=23 =8
No. of columns = m+ n=3+3= 6

 p q r p ∧ q p ∧ r (p ∧ q) ∨ (p ∧ r) T T T T T T T T F T F T T F T F T T T F F F F F F T T F F F F T F F F F F F T F F F F F F F F F

In the last column, the truth values of the statement is neither all T nor all F. Hence, it is neither a tautology nor a contradiction i.e. it is a contingency.

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#### APPEARS IN

2016-2017 (March) (with solutions)
Question 2.1.1 | 3.00 marks

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Solution Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency. Concept: Mathematical Logic - Truth Value of Statement in Logic.
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