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12th Standard English Medium Maths Subject Discrete Mathematics Book Back 5 Mark Questions with Solution Part -I

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. Using the equivalence property, show that p ↔️ q ≡ ( p ∧ q) v (ㄱp ∧ ㄱq)

  2. Verify whether the following compound propositions are tautologies or contradictions or contingency
    ((p⟶ q) ∧ (q ⟶ r)) ⟶ (p ⟶ r)

  3. Let M = \(\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) :x\in R-\{ 0\} \right\} \) and let * be the matrix multiplication. Determine whether M is closed under ∗. If so, examine the commutative and associative properties satisfied by ∗ on M.

  4. Let A be Q\{1}. Define ∗ on A by x*y = x + y − xy. Is ∗ binary on A? If so, examine the commutative and associative properties satisfied by ∗ on A.

  5. Check whether the statement p➝(q➝p) is a tautology or a contradiction without using the truth table.

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