" /> -->

Discrete Mathematics Model Question Paper 1

12th Standard EM

    Reg.No. :
  •  
  •  
  •  
  •  
  •  
  •  

Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. Subtraction is not a binary operation in

    (a)

    R

    (b)

    Z

    (c)

    N

    (d)

    Q

  2. Which one of the following statements has truth value F?

    (a)

    Chennai is in India or \(\sqrt 2\) is an integer

    (b)

    Chennai is in India or \(\sqrt 2\) is an irrational number

    (c)

    Chennai is in China or \(\sqrt 2\) is an integer

    (d)

    Chennai is in China or \(\sqrt 2\) is an irrational number

  3. Which one is the contrapositive of the statement (pVq)⟶r?

    (a)

    ㄱr➝(ㄱp∧ㄱq)

    (b)

    ㄱr⟶(p∨q)

    (c)

    r⟶(p∧q)

    (d)

    p⟶(q∨r)

  4. The Identity element of \(\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) \right\} \) |x\(\in \)R, x≠0} under matrix multiplication is

    (a)

    \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \)

    (b)

    \(\left( \begin{matrix} \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \\ \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \end{matrix} \right) \)

    (c)

    \(\left( \begin{matrix} \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \\ \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \end{matrix} \right) \)

    (d)

    \(\left( \begin{matrix} \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \\ \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \end{matrix} \right) \)

  5. Which of the following is a contradiction?

    (a)

    p v q

    (b)

    p ∧ q

    (c)

    q v ~ q

    (d)

    q ∧ ~ q

  6. 5 x 2 = 10
  7. How many rows are needed for following statement formulae?
    (( p ∧ q) ∨ (¬r ∨¬s)) ∧ (¬ t ∧ v))

  8. Determine whether ∗ is a binary operation on the sets given below.
    (A*v)=a√b is binary on R

  9. Construct the truth table for the following statements.
    ​​​​​​¬p ∧ ¬q

  10. Show that p v (q ∧ r) is a contingency.

  11. Let G = {1, w, w2) where w is a complex cube root of unity. Then find the universe of w2. Under usual multiplication.

  12. 5 x 3 = 15
  13. 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.

  14. Define an operation∗ on Q as follows:  a*b=\(\left( \frac { a+b }{ 2 } \right) \); a,b ∈Q. Examine the existence of identity and the existence of inverse for the operation * on Q.

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

  16. In (z, *) where * is defined by a * b = ab, prove that * is not a binary operation on z.

  17. Construct the truth table for (-p) v (q ∧ r)

  18. 4 x 5 = 20
  19. Establish the equivalence property connecting the bi-conditional with conditional: p ↔️ q ≡ (p ➝ q) ∧ (q⟶ p)

  20. Using the equivalence property, show that p ↔️ q ≡ ( p ∧ q) v (ㄱp ∧ ㄱq)

  21. Construct the truth table for (p ∧ q) v r.

  22. In (N, *) where * is defined by x * y = max (x, y) check the closure axion and identity anion.

*****************************************

TN 12th Standard EM Maths free Online practice tests

Reviews & Comments about 12th Maths Chapter 12 Discrete Mathematics Model Question Paper 1

Write your Comment