Existential Quantifier

Q. X: Rajat's students
P: Full marks in Maths
Q: Full marks in Economics

”Each of Rajat's students scored full in Maths or Economics” is written as .

1. ∀x∈X, P∨~Q
2. ∀x∈X, ~P∨Q
3. ∀x∈X, P∨Q
4. ∀x∈X, P∧Q

Q.

”Each of Rajat's students either scored distinction in chemistry or physics” is represented by which of the following expressions

X : set of Rajat's students

P : x scored distinction in chemistry

Q : x scored distinction in physics

1. ∀ x ∈ X, P ∧ Q

2. ∃ x ∈ X, P ∧ Q

3. ∀ x ∈ X, P ∨ Q

4. ∃ x ∈ X, P ∨ Q

Q. If $S_n=nP+\frac{n}{2}(n-1)$Q, where $S_n$ denotes the sum of first n terms of an AP, the common difference is

1. P + Q
2. 2P + 3Q
3. 2Q
4. Q

Q.

”Each of Rajat's students either scored distinction in chemistry or physics” is represented by which of the following expressions

X : set of Rajat's students

P : x scored distinction in chemistry

Q : x scored distinction in physics

1. $\exists xϵX,P\vee Q$

2. $\forall xϵX,P\wedge Q$

3. $\exists xϵX,P\wedge Q$

4. $\forall xϵX,P\vee Q$