A binary operation on a set S is a function from

(a)

S ⟶ S

(b)

(SxS) ⟶ S

(c)

S⟶ (SxS)

(d)

(SxS) ⟶ (SxS)

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

(a)

Q⁺

(b)

Z

(c)

R

(d)

C

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 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 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

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 binary operation * defined on a set s is said to be commutative if ______

(a)

a*b \(\in \) S ∀ a, b \(\in \) S

(b)

a*b = b*a ∀ a, b \(\in \) S

(c)

(a*b) * c = a*(b*c) ∀ a, b \(\in \) S

(d)

a*b = e ∀ a, b \(\in \) S

The number of binary operations that can be defined on a set of 3 elements is _____________

(a)

3²

(b)

3³

(c)

3⁹

(d)

3¹

Which of the following is a contradiction?

(a)

p v q

(b)

p ∧ q

(c)

q v ~ q

(d)

q ∧ ~ q

Let p: Kamala is going to school
q: There are 20 students in the class. Then Kamala is not going to school or there are 20 students in the class is represented by

(a)

p v q

(b)

p ∧ q

(c)

~ p

(d)

~ p v q