# Arunachal Pradesh PSC: Philosphy MCQs (Practice_Test 20 of 90)

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Match logical equivalents of the formulae in List-I and List-II and select the correct answer using the codes given below:

List-I List-II Formula (~ p ~ q)

Formula (~ p-~ q)

Formula ~ (p. ~ q)

Formula ~ (~ p-~ q)

Formula ~ (p q)

Formula ~ (p-q)

Formula ~ p-q

Formula (p. q)

- A
- B
- C
- D

- 3
- 1
- 4
- 2

- 2
- 3
- 4
- 1

- 2
- 1
- 3
- 4

- 1
- 2
- 3
- 4

Which one of the following sentences is the correct rendering of the symbolic sentence ‘[ (P-Q. R) ]-[S (T-U) ]’

If either plums or apricots are sweet and grapes are sour, then I'll have a glass of orange juice and either buy almonds or cashew-nuts

If either plums and apricots are sweet or grapes are sour, then I'll have a glass of orange juice and either buy almonds or cashew-nuts

If either plums are sweet or apricots and grapes are sour, then I'll have a glass of orange juice and buy almonds or cashew-nuts

If either plums are sweet or apricots and grapes are sour, then I'll have a glass of orange juice or buy almonds and cashew-nuts

Which one of the following statements will have a different symbolization?

The horse wins the race only if the horse is fast

That the horse is fast is a sufficient condition for the horse to win the race

That the horse is fast is a necessary condition for the horse to win the race

If the horse wins the race, the horse is fast

Consider the following equivalents:

~~ (~ p-~ q) -~ (p ~~ q)

[ (p-q) - (q-p) -~ (~ p-q). ~ (~ q-p) ]

(p-q) -~ (~~ p ~ q)

- (p ~ q) -~~ (~ p-~~ q)

The correct set of equivalents would be

1 and 2

1 and 3

2 and 3

2 and 4

Which one of the following is equivalent to p?

(p-q-r) (p-q-~ r). (p-~ q-r). (p-~ q-~ r).

(p-q) (p-r). (q-r). (~ p-r).

p (~ p-q) (q-p).

p- (~ p q) (q- (~ q. p). )

Consider the following tautologies:

~ (P-Q) - (P-~ Q)

(Q-P) -~ (P-Q)

~ (P-Q) - (Q-P)

(P-~ Q) -~ (Q-Q)

Which of the above tautologies are correct?

1 and 2

2 and 3

1 and 3

2 and 4

Which one of the following is a contraction?

( (p-q) -p) -~ p

( (p-q) -r) -- (p~ q)

~ q (p-q).

(p ~ q) - (~ p-q)

Consider the following proof of argument:

(A-B) -C

(C-B) -A- (D-E)

AxD/-D-E

A

A-B

C

C-B

A- (D-E)

D-E

Which set of rules of inference is involved in the above

Material Implication, Hypothetical Syllogism and Simplification

Modus Ponens, Simplifiation and Disjuctive Syllogism

Simplification, Addition and Modus Ponens

Simplification, Hypothetical Syllogism and Addition

From which one of the following is formally derivable?

1 (p-q). (r-s). 2. q-r 3. ~ r

1 (p-q). (r-s). 2. p ~ q 3. r-p

1 (p-q). (r-s). 2. p- (s-q) 3. ~ q

1 (pq). (r. s). 2. q- (s-p) 3. q

The argument A/-B-~ B is proved in the following way:

A

~ B-~ B

~ B ~~ B

B ~ B

B-~ B

The steps 1 to 5 constitute

A conditional proof

an indirect proof

a proof by transformation

no proof