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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on Discrete Mathematics Set 2
Q1 | The set O of odd positive integers less than 10 can be expressed by ___________ .
- {1, 2, 3}
- {1, 3, 5, 7, 9}
- {1, 2, 5, 9}
- {1, 5, 7, 9, 11}
Q2 | 8. The set of positive integers is _________ .
- infinite
- finite
- subset
- empty
Q3 | If p ˄ q is T, then
- p is t, q is t
- p is f, q is t
- p is f, q is f
- p is t, q is f
Q4 | If p →q is F, then
- p is t, q is t
- p is f, q is t
- p is f, q is f
- p is t, q is f
Q5 | The statement from ∼ (p ˄ q) is logically equivalent to
- ∼ p ˅ ∼ q
- ∼ p ˅ qc
- p ˅ ∼ q
- ∼ p ˄∼ q
Q6 | p → p is logically equivalent to
- p
- tautology
- contradiction
- none of these
Q7 | The converse of p → q is
- ∼q → ∼p
- ∼ p → ∼ q
- ∼ p → q
- q → p
Q8 | Let p: Mohan is rich, q : Mohan is happy, then the statement: Mohan is rich, but Mohan is not happy in symbolic form is
- p ˄ q
- ∼ p˄ q
- p ˅ q
- p ˄ ∼ q
Q9 | Let p: I will get a job, q: I pass the exam, then the statement form: I will get a job only if I pass the exam, in symbolic from is
- p → q
- p ˄ q
- q → p
- p ˄ q
Q10 | Let p denote the statement: “Gopal is tall”, q: “Gopal is handsome”. Then the negation of the statement Gopal is tall, but not handsome,in symbolic form is:
- ∼ p ˄q
- ∼ p ˅ q
- ∼ p ˅∼q
- ∼ p ˄∼q
Q11 | If p ˄ (p → q) is T, then
- p is t
- p is f, q is t
- p is t, q is t
- p is f, q is f
Q12 | If (∼ (p ˅ q)) → q is F, then
- p is t, q is f
- p is f, q is t
- p is t, q is t
- p is f, q is
Q13 | If (∼ p → r) ˄ (p ↔ q) is T and r is F, then truth values of p and q are:
- p is t, q is t
- p is t, q is f
- p is f, q is f
- p is f, q is t
Q14 | If ((p → q ) → q) → p is F, then
- p is t, q is t
- p is t, q is f
- p is f, q is t
- p is f, q is f
Q15 | (p ˄ (p → q )) → q is logically equivalent to
- p ˅ q
- (p ˄ q) ˅ (~ p˄ ~q)
- tautology
- (~ p ˅ q) ˄ (p ˅ q)
Q16 | If (p ˅ q) ˄ (~ p˅ ~q) is F, then
- p is t, q is t, or q is f
- p is f, q is t
- p is t, q is f
- p and q must have same truth values
Q17 | Let p denote the statement: “I finish my homework before dinner”, q: “It rains” and r: “I will go for a walk”, the representative of the following statement: if I finish my homework before dinner and it does not rain, then I will go for walk is
- p ˄ ~q ˄ r
- (p ˄ ~q )→ r
- p →(~q˄ r)
- (p →~q)→ r)
Q18 | The contrapositive of p →q is
- ~ q → ~ p
- ~ p → ~ qc
- ~ p → q
- ~ q → p
Q19 | Which of the following is declarative statement?
- it’s right
- three is divisible by 3.
- two may not be an even integer
- i love you
Q20 | Which of the proposition is p ^ (~p v q) is
- tautulogy
- contradiction
- logically equivalent to p ^ q
- all of above
Q21 | The relation R defined in A = {1, 2, 3} by aRb, ifa2 – b2£ 5. Which of the following is false?
- r = {(1, 1), (2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)}
- r–1 = r
- domain of r = {1, 2, 3}
- range of r = {5}
Q22 | The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) :x2 – y2< 16} is given by
- {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}
- {(2, 2), (3, 2), (4, 2), (2, 4)}
- {(3, 3), (4, 3), (5, 4), (3, 4)}
- none of the above
Q23 | If R = {x, y) : x, y Î Z, x2 + y2 £ 4} is a relation in z, then domain of R is
- {0, 1, 2}
- {– 2, – 1, 0}
- {– 2, – 1, 0, 1, 2}
- none of these
Q24 | If A = { (1, 2, 3}, then the relation R = {(2, 3)} in A is
- symmetric and transitive only
- symmetric only
- transitive only
- not transitive
Q25 | Let X be a family of sets and R be a relation in X, defined by ‘A is disjoint from B’. Then, R is
- reflexive
- symmetric
- anti-symmetric
- transitive