A binary operation on a set S is a function from

(a)

S ⟶ S

(b)

(SxS) ⟶ S

(c)

S⟶ (SxS)

(d)

(SxS) ⟶ (SxS)

Subtraction is not a binary operation in

(a)

R

(b)

Z

(c)

N

(d)

Q

Which one of the following is a binary operation on N?

(a)

Subtraction

(b)

Multiplication

(c)

Division

(d)

All the above

In the set R of real numbers ‘*’ is defined as follows. Which one of the following is not a binary operation on R?

(a)

a*b = min (a.b)

(b)

a*b = max (a, b)

(c)

a*b = a

(d)

a*b = a^b

The operation * defined by \(a * b =\frac{ab}{7}\) is not a binary operation on

(a)

Q⁺

(b)

Z

(c)

R

(d)

C

In the set Q define a⊙b = a+b+ab. For what value of y, 3⊙(y⊙5) = 7?

(a)

y = \(\frac{2}{3}\)

(b)

y = \(\frac{-2}{3}\)

(c)

y = \(\frac{-3}{2}\)

(d)

y = 4

If a * b=\(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \) on the real numbers then * is

(a)

commutative but not associative

(b)

associative but not commutative

(c)

both commutative and associative

(d)

neither commutative nor associative

Which one of the following statements has the truth value T?

(a)

sin x is an even function

(b)

Every square matrix is non-singular

(c)

The product of complex number and its conjugate is purely imaginary

(d)

\(\sqrt 5\) is an irrational number

Which one of the following statements has truth value F?

(a)

Chennai is in India or \(\sqrt 2\) is an integer

(b)

Chennai is in India or \(\sqrt 2\) is an irrational number

(c)

Chennai is in China or \(\sqrt 2\) is an integer

(d)

Chennai is in China or \(\sqrt 2\) is an irrational number

If a compound statement involves 3 simple statements, then the number of rows in the truth table is

(a)

9

(b)

8

(c)

6

(d)

3

Which one is the inverse of the statement (pVq)➝(pΛq)?

(a)

(p∧q)➝(pVq)

(b)

ᄀ(pvq)➝(p∧q)

(c)

(ᄀpvᄀq)➝(ᄀp∧ᄀq)

(d)

(ᄀp∧ᄀq)➝(ᄀpVᄀq)

Which one is the contrapositive of the statement (pVq)⟶r?

(a)

ㄱr➝(ㄱp∧ㄱq)

(b)

ㄱr⟶(p∨q)

(c)

r⟶(p∧q)

(d)

p⟶(q∨r)

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)

(a)	(b)	(c)	(d)
T	T	T	T

(b)

(a)	(b)	(c)	(d)
T	F	T	T

(c)

(a)	(b)	(c)	(d)
T	T	F	T

(d)

(a)	(b)	(c)	(d)
T	F	F	F

In the last column of the truth table for ¬( p ∨ ¬q) the number of final outcomes of the truth value 'F' are

(a)

1

(b)

2

(c)

3

(d)

4

Which one of the following is incorrect? For any two propositions p and q, we have

(a)

¬ (p∨q) ≡ ¬ p ∧ ¬q

(b)

¬ ( p∧ q)≡¬p ∨ ¬q

(c)

¬ (p ∨ q)≡¬p∨¬q

(d)

¬(¬p)≡ p

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)

(a)	(b)	(c)	(d)
T	T	T	T

(b)

(a)	(b)	(c)	(d)
F	T	T	T

(c)

(a)	(b)	(c)	(d)
F	F	T	T

(d)

(a)	(b)	(c)	(d)
T	T	T	F

The dual of ᄀ(p V q) V [p V (p ∧ ᄀr)] is

(a)

ᄀ(p ∧ q) ∧ [p V (p ∧ ᄀr)]

(b)

(p ∧ q) ∧ [p ∧ (p V ᄀr)]

(c)

ᄀ(p ∧ q) ∧ [p ∧ (p ∧ r)]

(d)

ᄀ(p ∧ q) ∧ [p ∧ (pV ᄀr)]

The proposition p ∧ (¬p ∨ q) is

(a)

a tautology

(b)

a contradiction

(c)

logically equivalent to p ∧ q

(d)

logically equivalent to p ∨ q

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)

(a)	(b)	(c)	(d)
F	T	F	T

(b)

(a)	(b)	(c)	(d)
T	F	T	F

(c)

(a)	(b)	(c)	(d)
T	T	F	F

(d)

(a)	(b)	(c)	(d)
F	F	T	T

Which one of the following is not true?

(a)

Negation of a negation of a statement is the statement itself

(b)

If the last column of the truth table contains only T then it is a tautology.

(c)

If the last column of its truth table contains only F then it is a contradiction

(d)

If p and q are any two statements then p↔️q is a tautology.