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Published on: 01/06/2021
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Questions + Answers key
Take MCQ Maths Test1.
Which one of the following is not true?
Negation of a negation of a statement is the statement itself
If the last column of the truth table contains only T then it is a tautology.
If the last column of its truth table contains only F then it is a contradiction
If p and q are any two statements then p↔️q is a tautology.
2.
Determine the truth value of each of the following statements:
(a) 4 + 2 = 5 and 6 + 3 = 9
(b) 3 + 2 = 5 and 6 + 1 = 7
(c) 4 + 5 = 9 and 1 + 2 = 4
(d) 3 + 2 = 5 and 4 + 7 = 11
| (a) | (b) | (c) | (d) |
| F | T | F | T |
| (a) | (b) | (c) | (d) |
| T | F | T | F |
| (a) | (b) | (c) | (d) |
| T | T | F | F |
| (a) | (b) | (c) | (d) |
| F | F | T | T |
3.
The proposition p ∧ (¬p ∨ q) is
a tautology
a contradiction
logically equivalent to p ∧ q
logically equivalent to p ∨ q
4.
The dual of ᄀ(p V q) V [p V (p ∧ ᄀr)] is
ᄀ(p ∧ q) ∧ [p V (p ∧ ᄀr)]
(p ∧ q) ∧ [p ∧ (p V ᄀr)]
ᄀ(p ∧ q) ∧ [p ∧ (p ∧ r)]
ᄀ(p ∧ q) ∧ [p ∧ (pV ᄀr)]
5.
| p | q | (p ∧ q) ⟶ ¬q |
| T | T | (a) |
| T | F | (b) |
| F | T | (c) |
| F | F | (d) |
Which one of the following is correct for the truth value of (p ∧ q)⟶ ¬p?
| (a) | (b) | (c) | (d) |
| T | T | T | T |
| (a) | (b) | (c) | (d) |
| F | T | T | T |
| (a) | (b) | (c) | (d) |
| F | F | T | T |
| (a) | (b) | (c) | (d) |
| T | T | T | F |
6.
Which one of the following is incorrect? For any two propositions p and q, we have
¬ (p∨q) ≡ ¬ p ∧ ¬q
¬ ( p∧ q)≡¬p ∨ ¬q
¬ (p ∨ q)≡¬p∨¬q
¬(¬p)≡ p
7.
In the last column of the truth table for ¬( p ∨ ¬q) the number of final outcomes of the truth value 'F' are
1
2
3
4
8.
The truth table for (p ∧ q) ∨ ¬q is given below
| p | q | (p ∧ q) ∨ (¬q) |
| T | T | (a) |
| T | F | (b) |
| F | T | (c) |
| F | F | (d) |
Which one of the following is true?
| (a) | (b) | (c) | (d) |
| T | T | T | T |
| (a) | (b) | (c) | (d) |
| T | F | T | T |
| (a) | (b) | (c) | (d) |
| T | T | F | T |
| (a) | (b) | (c) | (d) |
| T | F | F | F |
9.
10.
11.
If a compound statement involves 3 simple statements, then the number of rows in the truth table is
9
8
6
3
12.
Which one of the following statements has truth value F?
Chennai is in India or \(\sqrt 2\) is an integer
Chennai is in India or \(\sqrt 2\) is an irrational number
Chennai is in China or \(\sqrt 2\) is an integer
Chennai is in China or \(\sqrt 2\) is an irrational number
13.
Which one of the following statements has the truth value T?
sin x is an even function
Every square matrix is non-singular
The product of complex number and its conjugate is purely imaginary
\(\sqrt 5\) is an irrational number
14.
15.
In the set Q define a⊙b = a+b+ab. For what value of y, 3⊙(y⊙5) = 7?
y = \(\frac{2}{3}\)
y = \(\frac{-2}{3}\)
y = \(\frac{-3}{2}\)
y = 4
16.
The operation * defined by \(a * b =\frac{ab}{7}\) is not a binary operation on
Q+
Z
R
C
17.
In the set R of real numbers ‘*’ is defined as follows. Which one of the following is not a binary operation on R?
a*b = min (a.b)
a*b = max (a, b)
a*b = a
a*b = ab
18.
Which one of the following is a binary operation on N?
Subtraction
Multiplication
Division
All the above
19.
20.
A binary operation on a set S is a function from
S ⟶ S
(SxS) ⟶ S
S⟶ (SxS)
(SxS) ⟶ (SxS)
1.
(d)
If p and q are any two statements then p↔️q is a tautology.
2.
(a)
| (a) | (b) | (c) | (d) |
| F | T | F | T |
3.
(c)
logically equivalent to p ∧ q
4.
(d)
ᄀ(p ∧ q) ∧ [p ∧ (pV ᄀr)]
5.
(b)
| (a) | (b) | (c) | (d) |
| F | T | T | T |
6.
(c)
¬ (p ∨ q)≡¬p∨¬q
7.
(c)
3
8.
(c)
| (a) | (b) | (c) | (d) |
| T | T | F | T |
9.
(b)
10.
(c)
11.
(b)
8
12.
(c)
Chennai is in China or \(\sqrt 2\) is an integer
13.
(d)
\(\sqrt 5\) is an irrational number
14.
(a)
15.
(b)
y = \(\frac{-2}{3}\)
16.
(b)
Z
17.
(d)
a*b = ab
18.
(b)
Multiplication
19.
(c)
20.
(b)
(SxS) ⟶ S
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