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Phoenix Institute of Mathematics, Revision Test, Std: Mathematics (12th), Date : 21/Oct/2021, , Subject: Mathematics & Statistics, , Time: 60Min, Max Marks: 25, , Section A (MCQ & VSA Questions), Q.1, Select and write the correct answer:, (i) What is the contrapositive of a → b?, D) ~ b → a, A) ~ a → ~ b B) b → a C) ~ b → ~ a, (ii) What is the inverse of q → p?, A) p → ~ q B) ~ p → q C) ~ q → p, D) ~ q → ~ p, Q.2, Answer the following:, (i) Write the negations of the following statement: ∀x ∈N, 2x + 3 is odd, (ii) Write the negation of the following: Price increases, (iii) If statement p, q is true and r, s are false, determine the truth values of the following: (~p → q) Λ (r, ↔ s), Section B (2 MARKS EACH), Attempt any Four:, Q.3, Construct the truth table for following statement pattern: (p ∨ ~ q) → (r Λ p), Construct the truth table for following statement pattern: p → (q → p), Q.4, Q.5, Using rules of negation write the negations of the following with justification: (~ p ∨ ~ q) ∨ (p Λ ~ q), Q.6, Construct the truth table for following statement pattern: (q → p) ∨ (~ p ↔ q), Q.7, Using rules of negation write the negations of the following with justification: ~ (p Λ q) ∨ (p ∨ ~ q), Q.8, Construct the truth table for following statement pattern: (p Λ q) ↔ (q ∨ r), Section C (3 MARKS EACH), Attempt any Two:, Construct the truth table for the following: [(p Λ q) ∨ r] Λ [~ r ∨ (p Λ q)], Q.9, Q.10, Construct the truth table for the following: ~ (~ p Λ ~ q) ∨ q, Examine whether following statement pattern is a tautology or a contradiction or a contingency: [(p, Q.11, → q) Λ ~ q] → ~ p, Section D (4 MARKS EACH), Attempt any One:, Q.12, Without using truth table prove that: p ↔ q ≡ (p Λ q)∨ (~ p Λ ~ q), Q.13, Construct the truth table for following statement pattern:[(~ p ∨ q) Λ (q → r)] → (p → r), -------- All the Best --------, , 4, , 3, , 8, , 6, , 4, , Page 1 of 1