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

12th Standard

    Reg.No. :
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Maths

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

    3 Marks

    10 x 3 = 30
  1. Verify the
    (i) closure property,
    (ii) commutative property,
    (iii) associative property
    (iv) existence of identity and
    (v) existence of inverse for the arithmetic operation + on Z.

  2. Verify the
    (i) closure property,
    (ii) commutative property,
    (iii) associative property
    (iv) existence of identity and
    (v) existence of inverse for the arithmetic operation - on Z.

  3. Verify the
    (i) closure property,
    (ii) commutative property,
    (iii) associative property
    (iv) existence of identity and
    (v) existence of inverse for the arithmetic operation + on Ze = the set of all even integers

  4. Verify 
    (i) closure property  
    (ii) commutative property, and 
    (iii) associative property of the following operation on the given set. (a*b) = ab;∀a, b∈N (exponentiation property)

  5. How many rows are needed for following statement formulae?
    \(p \vee \neg t \wedge(p \vee \neg s)\)

  6. How many rows are needed for following statement formulae?
    (( p ∧ q) ∨ (¬r ∨¬s)) ∧ (¬ t ∧ v))

  7. Consider p→q : If today is Monday, then 4 + 4 = 8.

  8. Write down the
    (i) conditional statement
    (ii) converse statement
    (iii) inverse statement, and
    (iv) contrapositive statement for the two statements p and q given below.
    p: The number of primes is infinite.
    q: Ooty is in Kerala.

  9. Construct the truth table for \((p\overset { \_ \_ }{ \vee } q)\wedge (p\overset { \_ \_ }{ \vee } \neg q)\)

  10. 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 AVB

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