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12th Standard English Medium Maths Subject Discrete Mathematics Book Back 3 Mark Questions with Solution Part -II

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 30

    3 Marks

    10 x 3 = 30
  1. Establish the equivalence property p ➝ q ≡ ㄱp ν q

  2. Let \(A=\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \end{matrix}\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix} \right) ,B=\left( \begin{matrix} 0 & 1 \\ 1 & 0 \\ 1 & 0 \end{matrix}\begin{matrix} 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix} \right) ,C=\left( \begin{matrix} 1 & 1 \\ 0 & 1 \\ 1 & 1 \end{matrix}\begin{matrix} 0 & 1 \\ 1 & 0 \\ 1 & 1 \end{matrix} \right) \)be any three boolean matrices of the same type.
    Find AΛB

  3. Verify whether the following compound propositions are tautologies or contradictions or contingency
    (p ∧ q) ∧ ¬ (p ∨ q)

  4. Let \(A=\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \end{matrix}\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix} \right) ,B=\left( \begin{matrix} 0 & 1 \\ 1 & 0 \\ 1 & 0 \end{matrix}\begin{matrix} 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix} \right) ,C=\left( \begin{matrix} 1 & 1 \\ 0 & 1 \\ 1 & 1 \end{matrix}\begin{matrix} 0 & 1 \\ 1 & 0 \\ 1 & 1 \end{matrix} \right) \)be any three boolean matrices of the same type.
    Find (A∧B)∨C

  5. Verify whether the following compound propositions are tautologies or contradictions or contingency
    (( p V q)∧ ¬ p) ➝ q

  6. Verify whether the following compound propositions are tautologies or contradictions or contingency
    ( p ⟶ q) ↔️ (~ p ⟶ q)

  7. Show that ¬( p ∧ q) ≡ ¬p V ¬q

  8. Prove that q ➝ p ≡ ¬p ➝ ¬q

  9. Show that p ➝ q and q ➝ p are not equivalent

  10. Show that ¬(p↔️q) ≡ p↔️¬q

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