Discrete Mathematics Practice Test 1

1. The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.

∀x(C(x) ∧ F (x))

∃x(C(x) ∧ F (x))

∀x(C(x) → F (x))

∃x(C(x) → F (x))

2. In this circuit shown the lamp will be glowing if _________

P: False, Q: False, R: True

P: True, Q: True, R: True

P: True, Q: True, R: False

None of the mentioned

3. Let A: “010101”, B=?, If { A (Ex-or) B } is a resultant string of all ones then which of the following statement regarding B is correct?

All of the mentioned

{A (and) B} is a resultant string having all zeroes

B is negation of A

B is 101010

4. A compound proposition that is always ___________ is called a contradiction.

True

False

5. Use quantifiers and predicates with more than one variable to express, “There is a pupil in this lecture who has taken at least one course in Discrete Maths.”

∀x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class

∃x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures

6. What is the dual of (A ∧ B) v (C ∧ D)?

(A V B) v (C ∧ D)

(A V B) v (C v D)

(A ∧ B) v (C v D)

(A V B) ^ (C v D)

7. “Parul is out for a trip or it is not snowing” and “It is snowing or Raju is playing chess” imply that __________

Raju is playing chess

Parul is out for a trip and Raju is playing chess

Parul is out for a trip or Raju is playing chess

Parul is out for trip

8. What rule of inference is used in this argument?
“If I go for a balanced diet, then I will be fit. If I will be fit, then I will remain healthy. Therefore, if I go for a balanced diet, then I will remain healthy.”

Hypothetical syllogism

Modus tollens

Disjunctive syllogism

Modus ponens

9. Let P(x) denote the statement “x = x + 7.” What is the truth value of the quantification ∃xP(x), where the domain consists of all real numbers?

False

True

10. The premises (p ∧ q) ∨ r and r → s imply which of the conclusion?

p ∨ r

p ∨ q

q ∨ r

p ∨ s