# Competitive Exams: 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