Discrete Mathematics Set 12

Computer Science Engineering (CSE)

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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on Discrete Mathematics Set 12

Q1 | a ⊕ b =                  
  • (a+b)(a`+b`)
  • (a+b`)
  • b`
  • a` + b`
Answer: (a+b)(a`+b`)
Q2 | Find the simplified expression A’BC’+AC’.
  • b
  • a+c
  • (a+b)c’
  • b’c
Answer: (a+b)c’
Q3 | Evaluate the expression: (X + Z)(X + XZ’)+ XY + Y.
  • xy+z’
  • y+xz’+y’z
  • x’z+y
  • x+y
Answer: x+y
Q4 | Simplify the expression: A’(A + BC) + (AC + B’C).
  • (ab’c+bc’)
  • (a’b+c’)
  • (a+ bc)
  • ac
Answer: (a’b+c’)
Q5 | What is the simplification value of MN(M+ N’) + M(N + N’)?
  • m
  • mn+m’n’ c) (1+m)
  • d
  • m+n’
Answer: mn+m’n’ c) (1+m)
Q6 | Simplify the expression XZ’ + (Y + Y’Z) + XY.TOPIC 5.5 MINIMIZATION OF BOOLEAN ALGEBRA
  • (1+xy’)
  • yz + xy’ + z’
  • (x + y +z)
  • xy’+ z’
Answer: (x + y +z)
Q7 | Find the simplified term Y’ (X’ + Y’) (X + X’Y)?
  • xy’
  • x’y
  • x + y
  • x’y’
Answer: xy’
Q8 | If an expression is given that x+x’y’z=x+y’z, find the minimal expression of the function F(x,y,z) = x+x’y’z+yz?
  • y’ + z
  • xz + y’
  • x + z
  • x’ + y
Answer: x + z
Q9 | Simplify the expression: XY’ + X’ + Y’X’.
  • x’ + y
  • xy’
  • (xy)’
  • y’ + x
Answer: (xy)’
Q10 | Minimize the Boolean expression using Boolean identities: A′B+ABC′+BC’+AB′C′.
  • b(ac)’ + ac’
  • ac’ + b’
  • abc + b’ + c
  • bc’ + a’b
Answer: b(ac)’ + ac’
Q11 | Minimize the following Boolean expression using Boolean identities. F(A,B,C) = (A+BC’)(AB’+C)
  • a + b + c’
  • ac’ + b
  • b + ac
  • a(b’ + c)
Answer: a(b’ + c)
Q12 | Which of the following statement is a proposition?
  • Get me a glass of milkshake
  • God bless you!
  • What is the time now?
  • The only odd prime number is 2
Answer: The only odd prime number is 2
Explaination:
Only this statement has got the truth value which is false.
Q13 | The truth value of ‘4+3=7 or 5 is not prime’.
  • False
  • True
Answer: True
Explaination:
Compound statement with ‘or’ is true when either of the statement is true. Here the first part of the statement is true, hence the whole is true.
Q14 | Which of the following option is true?
  • If the Sun is a planet, elephants will fly
  • 3 +2 = 8 if 5-2 = 7
  • 1 > 3 and 3 is a positive integer
  • -2 > 3 or 3 is a negative integer
Answer: If the Sun is a planet, elephants will fly
Explaination:
Hypothesis is false, thus the whole statement is true.
Q15 | What is the value of x after this statement, assuming the initial value of x is 5?‘If x equals to one then x=x+2 else x=0’.
  • 1
  • 3
  • 2
Explaination:
If condition is false so value decided according to else condition.
Q16 | Let P: I am in Bangalore.; Q: I love cricket.; then q -> p(q implies p) is?
  • If I love cricket then I am in Bangalore
  • If I am in Bangalore then I love cricket
  • I am not in Bangalore
  • I love cricket
Answer: If I love cricket then I am in Bangalore
Explaination:
Q is hypothesis and P is conclusion. So the compound statement will be if hypothesis then conclusion.
Q17 | Let P: If Sahil bowls, Saurabh hits a century.; Q: If Raju bowls, Sahil gets out on first ball. Now if P istrue and Q is false then which of the following can be true?
  • Raju bowled and Sahil got out on first ball
  • Raju did not bowled
  • Sahil bowled and Saurabh hits a century
  • Sahil bowled and Saurabh got out
Answer: Sahil bowled and Saurabh hits a century
Explaination:
Either hypothesis should be false or both (hypothesis and conclusion) should be true.
Q18 | The truth value ‘9 is prime then 3 is even’.
  • False
  • TTru
Answer: TTru
Explaination:
The first part of the statement is false, hence whole is true.
Q19 | Let P: We should be honest., Q: We should be dedicated., R: We should be overconfident. Then ‘Weshould be honest or dedicated but not overconfident.’ Is best represented by?
  • ~P V ~Q V R
  • P ∧ ~Q ∧ R
  • P V Q ∧ R
  • P V Q ∧ ~R
Answer: P V Q ∧ ~R
Explaination:
The third part of the statement is negated, hence negation operator is used, for (‘or’ –V) is used and for(’but’- ∧).
Q20 | If there are n distinct components in a statement then there are _______ combinations ofvalues in the truth table.
  • 2^n
  • n+1
  • n
  • n+2
Answer: 2^n
Q21 | If P then Q is called _________ statement
  • Conjunction
  • disjunction
  • conditional
  • bi conditional
Answer: conditional
Q22 | (P->Q)-> (^Q) is __________.
  • not a well formed formula
  • tautology
  • contradiction
  • well formed formula
Answer: not a well formed formula
Q23 | A relation R in a set X is symmetric if ________.
  • xRy, yRz => xRz.
  • xRy
  • xRy=>yRx
  • xRx
Answer: xRy=>yRx
Q24 | If a relation is reflexive, then all the diagonal entries in the relation matrix must be________.
  • 0
  • 1
  • 2
  • -1
Answer: 1
Q25 | If R is reflexive, symmetric and transitive then the relation is said to be ________.
  • Binary relation
  • Compatibility relation
  • Equivalence relation
  • Partial order relation
Answer: Equivalence relation
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