Worksheets Class 11 Mathematics Mathematical Reasoning

Students should refer to Worksheets Class 11 Mathematics Mathematical Reasoning Chapter 14 provided below with important questions and answers. These important questions with solutions for Chapter 14 Mathematical Reasoning have been prepared by expert teachers for Class 11 Mathematics based on the expected pattern of questions in the class 11 exams. We have provided Worksheets for Class 11 Mathematics for all chapters on our website. You should carefully learn all the important examinations questions provided below as they will help you to get better marks in your class tests and exams.

Mathematical Reasoning Worksheets Class 11 Mathematics

Question. Which of the following is always true?                
(a) ( p⇒q) ≡ ~ q⇒~ p
(b) ~ ( p ∨ q) ≡ ∨ p ∨ ~ q
(c) ~ ( p⇒q) ≡ p ∧ ~ q
(d) ~ ( p ∨ q) ≡ ~ p ∧ ~ q

Question. The logically equivalent proposition of p⇔ q is:
(a) ( p ∧ q) ∨ ( p ∧ q)
(b) ( p⇒q) ∧ (q⇒ p)
(c) ( p ∧ q)∨ (q⇒ p)
(d) ( p ∧ q)⇒(q ∨ p)

Question. Which of the following is not a proposition?
(a) 3 is a prime
(b) 2 is irrational
(c) Mathematics is interesting
(d) 5 is an even integer

Question. ( p ∧ ~ q) ∧ (~ p ∧ q) is:
(a) A tautology
(b) A contradiction
(c) Both a tautology and a contradiction
(d) Neither a tautology nor a contradiction

Question. ~ p ∧ q is logically equivalent to:
(a) p →q
(b) q → p
(c) ~ ( p→q)
(d) ~ (q→ p)

Question. Which of the following is the inverse of the proposition: “If a number is a prime then it is odd?”
(a) If a number is not a prime then it is odd
(b) If a number is not a prime then it is odd
(c) If a number is not odd then it is not a prime
(d) If a number is not odd then it is a prime

Question. Which of the following is not a statement?
(a) Roses are red
(b) New Delhi is in India
(c) Every square is a rectangle
(d) Alas! I have failed

Question. Which of the following is not a statement?
(a) Every set is a finite set
(b) 8 is less than 6
(c) Where are you going?
(d) The sum of interior angles of a triangle is 180 degrees

Question. Sum of the two binary numbers (1000010)₂ and (11011)₂ is:
(a) (111101)₂
(b) (111111)₂
(c) (101111)₂
(d) (111001)2

Question. The truth-table given below is for which gate:
A 0 0 1 1
B 0 1 0 1
C 1 1 1 0
(a) XOR
(b) OR
(c) AND
(d) NAND

Question. Which of the following is not a statement?
(a) Please do me a favour
(b) 2 is an even integer
(c) 2 + 1 = 3
(d) The number 17 is prime

Question. Which of the following is not a statement?
(a) Give me a glass of water
(b) Asia is a continent
(c) The earth revolved round the sun
(d) The number 6 has two prime factors 2, 3

Question. Which of the following is an open statement?
(a) x is a natural number
(b) Give me a glass of water
(c) Wish you best of luck
(d) Good morning to all

Question. Negation is “2 + 3 = 5 and 8 < 10” is
(a) 2 + 3 ≠ 5 and < 10
(b) 2 + 3 = 5 and 8 ≮ 10
(c) 2 + 3 ≠ 5 or 8 ≮ 10
(d) None of these

Question. An OR gate is the Boolean function defined of :
(a) f (x₁ , x₂) = x₁ ∧ x₂ ; x₁ , x₂ ∈{0,1}
(b) f (x₁ ,x₂) = x₁ ∨ x₂ ; x₁ , x₂ ∈{0,1}
(c) f (x₁ , x₂) = x₁ ; x₁ , x ∈{0,1}
(d) f (x₁ , x₂ ) = x₁ ; x , x ∈{0,1}

Question. A NOT gate is the Boolean function defined by:
(a) f (x) = x, x∈{0,1}
(b) f (x) = x′, x∈{0,1}
(c) f (x) = x + x′, x∈{0,1}
(d) None of these

Question. p⇒ q can also be written as:
(a) p⇒ ~ q
(b) ~ p ∨ q
(c) ~ q⇒~ p
(d) None of these

Question. If p, q, r are simple propositions with truth values T, F, T, then the truth value of (~ p ∨ q) ∧ ~ r⇒ p is:
(a) True
(b) False
(c) True if r is false
(d) True if q is true

Question. If ( p ∧ ~ r)⇒(q ∨ r) is false and q and r are both false, then p is:
(a) True
(b) False
(c) May be true or false
(d) Data insufficient

Question. If p, q, r are simple propositions, then (p ∧ q)∧ (q ∧ r) is true then
(a) p, q, r are all false
(b) p, q, r are all true
(c) p, q are true and r is false
(d) p is true and q and r are false

Question. ~ ( p⇒q)⇔~ p ∨ ~ q is:
(a) A tautology
(b) A contradiction
(c) Neither a tautology nor a contradiction
(d) Cannot come to any conclusion

Question. ( p ∧ ~ q) ∧ (~ p ∨ q) is:
(a) A contradiction
(b) A tautology
(c) Either A or B
(d) Neither A nor B

Question. The truth table shown in figure is for:
A  0  0  1  1
B  0  1  0  1
Y  1  0  0  1
(a) XOR
(b) AND
(c) XNOR
(d) OR

Question. Which of the following is not logically equivalent to the proposition: “A real number is either rational or irrational”?
(a) If a number is neither rational nor irrational then it is not real
(b) If a number is not a rational or not an irrational, then it is not real
(c) If a number is not real, then it is neither rational nor irrational
(d) If a number is real, then it is rational or irrational

Question. If p: It rains today, q : I go to school, r : I shall meet any friends and s : I shall go for a movie, then which of the following is the proposition:
If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
(a) ~ ( p ∧ q)⇒(r ∧ s)
(b) ~ ( p ∧ ~ q)⇒(r ∧ s)
(c) ~ ( p ∧ q)⇒(r ∨ s)
(d) None of these

Question. Which of the following is not a logical statement?
(a) Two plus two equals four
(b) The sum of two positive numbers is positive
(c) Tomorrow is Friday
(d) Every equilateral triangle is an isosceles triangle.

Question. Which of the following is a logical statement?
(a) She is a Mathematics graduate
(b) There are 40 days in a moth
(c) How far is Chandigarh from here?
(d) Mathematics is fun.

Question. The negation of the compound proposition p ∨ (~ p ∨ q) is:
(a) ( p ∧ ~ q) ∧ ~ p
(b) ( p ∧ ~ q) ∨ ~ p
(c) ( p ∨ ~ q) ∨ ~ p
(d) None of these

Question. Which of the following is true?
(a) p⇒ q ≡ ~ p⇒ ~ q
(b) ~ ( p⇒~ q) ≡ ~ p ∧ q
(c) ~ (~ p⇒~ q) ≡~ p ∧ q
(d) ~ ( p⇔q) ≡ [~ ( p⇒q)∧ ~ (q⇒ p)]

Question. In a Boolean Algebra B, for all x in B, 0′ is equal to:
(a) 0
(b) 1
(c) x.0
(d) None of these

Question. In a Boolean Algebra B, for all x in B, 1′ = ?
(a) 0
(b) 1
(c) x ∧1
(d) None of these

Question. The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth”, is
(a) or
(b) Earth
(c) Sun
(d) and

Question. The negation of the statement “A circle is an ellipse”, is
(a) An ellipse is a circle
(b) An ellipse is not a circle
(c) A circle is not an ellipse
(d) None of these

Question. Dual of (x′∨ y′)′ = x ∧ y is:
(a) (x′∨ y′) = x ∨ y
(b) (x′∧ y′)′ = x ∨ y
(c) (x′∧ y′)′ = x ∧ y
(d) None of these

Question. Dual of x ∨ (y ∧ x) = x is:
(a) x ∧ (y ∨ x) = x
(b) x ∧ (y ∧ x) = x
(c) (x ∨ y) ∧ (x ∨ x) = x
(d) None of these

Question. (a) p∨ p′ = 0
(b) p ∧ p′ =1
(c) p ∨ p′ =1
(d) None of these

Question. (a) p ∧ p′ =1
(b) p ∧ p′ = 0
(c) p ∨ p′ = 0
(d) None of these

Question. (a) a ∨ a = 0
(b) a ∨ a = a
(c) a ∨1 = a
(d) None of these

Question. The contrapositive of ( p ∨ q)⇒r is:
(a) r⇒( p ∨ q)
(b) ~ r ⇒( p ∨ q)
(c) ~ r ⇒ ~ p ∧ ~ q
(d) p⇒(q ∨ r)

Question. If p⇒(q ∨ r) is false, then the truth values of p, q, r are respectively:
(a) T, F, F
(b) F, F, F
(c) F, T, T
(d) T, T, F