Inequalities Quiz Set 038

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Question 1

In a certain language different symbols represent different operators as follows.

  1. ∂ means X = Y
  2. ∏ means X ≤ Y
  3. Ξ means X ≥ Y
  4. √ means X < Y
  5. ∇ means X > Y

Statements: T ∇ U; U ∂ V; V √ W;

Conclusions:

  1. T ∇ V
  2. U Ξ W
 A

both I and II are true.

 B

only conclusion II is true.

 C

only conclusion I is true.

 D

either I or II can be true.

Soln.
Ans: c

The statements can be translated to T > U = V < W. Conclusion I translates to T > V. Conclusion II translates to U ≥ W. So we can see that only conclusion I is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

Solution | Discuss! | Chapters»

Question 2

In a certain language different symbols represent different operators as follows.

  1. Θ means X = Y
  2. ⊗ means X ≯ (not more than) Y
  3. ∀ means X ≮ (not less than) Y
  4. ∧ means X < Y
  5. Δ means X > Y

Statements: N ∧ O; O Δ P; P ⊗ Q;

Conclusions:

  1. N Δ P
  2. N ∧ Q
 A

both I and II are true.

 B

only conclusion II is true.

 C

only conclusion I is true.

 D

neither I nor II is true.

Soln.
Ans: d

The statements can be translated to N < O > P ≤ Q. Conclusion I translates to N > P. Conclusion II translates to N < Q. So we can see that neither I nor II is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

Solution | Discuss! | Chapters»

Question 3

In a certain language different symbols represent different operators as follows.

  1. ∩ means X = Y
  2. ≅ means X ≤ Y
  3. ¢ means X ≥ Y
  4. η means X < Y
  5. ∏ means X > Y

Statements: I η J; J ∏ K; K η L;

Conclusions:

  1. I η J
  2. J η L
 A

both I and II are true.

 B

only conclusion II is true.

 C

only conclusion I is true.

 D

either I or II can be true.

Soln.
Ans: c

The statements can be translated to I < J > K < L. Conclusion I translates to I < J. Conclusion II translates to J < L. So we can see that only conclusion I is true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

Solution | Discuss! | Chapters»

Question 4

In a certain language different symbols represent different operators as follows.

  1. ⊗ means X = Y
  2. © means X ≤ Y
  3. ∂ means X ≥ Y
  4. % means X < Y
  5. ∩ means X > Y

Statements: J ⊗ K; K ⊗ L; L ∩ M; M ∩ N;

Conclusions:

  1. M % K
  2. N ∩ L
  3. J ∩ M

Which of the above conclusions is/are true?

 A

both I and III.

 B

I only.

 C

II only.

 D

III only.

Soln.
Ans: a

The statements can be translated to J = K = L > M > N.

The conclusions translate to:

  1. M < K(True)
  2. N > L(False)
  3. J > M(True)
Solution | Discuss! | Chapters»

Question 5

In a certain language different symbols represent different operators as follows.

  1. √ means X = Y
  2. λ means X ≤ Y
  3. £ means X ≥ Y
  4. $ means X < Y
  5. ∇ means X > Y

Statements: D $ E; E $ F; F ∇ G; G $ H;

Conclusions:

  1. F ∇ H
  2. G ∇ E
  3. D $ H

Which of the above conclusions is/are true?

 A

Neither of the three.

 B

I only.

 C

II only.

 D

III only.

Soln.
Ans: a

The statements can be translated to D < E < F > G < H.

The conclusions translate to:

  1. F > H(False)
  2. G > E(False)
  3. D < H(False)
Solution | Discuss! | Chapters»
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Updated on 2020-02-07. Published on: 2016-04-13

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