Inequalities Quiz Set 028

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Question 1

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

  1. ® means X = Y
  2. ¥ means X ≯ (not more than) Y
  3. ¢ means X ≥ Y
  4. ω means X < Y
  5. µ means X > Y

Statements: G ¢ H; H µ I; I ¥ J;

Conclusions:

  1. H µ J
  2. G µ J
 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 G ≥ H > I ≤ J. Conclusion I translates to H > J. Conclusion II translates to G > J. 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 2

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: F @ G; G @ H; H © I; I ∀ J;

Conclusions:

  1. J ∀ G
  2. F © H
  3. I ∀ F

Which of the above conclusions is/are true?

 A

III only.

 B

both III and II.

 C

II only.

 D

I only.

Soln.
Ans: a

The statements can be translated to F = G = H < I > J.

The conclusions translate to:

  1. J > G(False)
  2. F < H(False)
  3. I > F(True)
Solution | Discuss! | Chapters»

Question 3

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

  1. µ means X = Y
  2. ¢ means X ≤ Y
  3. ∧ means X ≥ Y
  4. © means X < Y
  5. ρ means X > Y

Statements: N © O; O µ P; P ρ Q; Q ρ R;

Conclusions:

  1. R © O
  2. Q © O
  3. P © N

Which of the above conclusions is/are true?

 A

both I and II.

 B

I only.

 C

II only.

 D

III only.

Soln.
Ans: a

The statements can be translated to N < O = P > Q > R.

The conclusions translate to:

  1. R < O(True)
  2. Q < O(True)
  3. P < N(False)
Solution | Discuss! | Chapters»

Question 4

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

  1. ® means X = Y
  2. ∀ means X ≯ (not more than) Y
  3. ¥ means X ≮ (not less than) Y
  4. ∇ means X < Y
  5. @ means X > Y

Statements: D @ E; E ∇ F; F ¥ G;

Conclusions:

  1. F @ G
  2. F ® G
 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: d

The statements can be translated to D > E < F ≥ G. Conclusion I translates to F > G. Conclusion II translates to F = G. So we can see that either I or II can be true.

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

Solution | Discuss! | Chapters»

Question 5

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

  1. ⊗ means X = Y
  2. ρ means X ≤ Y
  3. ¥ means X ≥ Y
  4. ∃ means X < Y
  5. Δ means X > Y

Statements: L ⊗ M; M ⊗ N; N ⊗ O; O ⊗ P;

Conclusions:

  1. P ∃ N
  2. O ∃ M
  3. M ⊗ P

Which of the above conclusions is/are false?

 A

All.

 B

both I and II.

 C

II only.

 D

both II and III.

Soln.
Ans: b

The statements can be translated to L = M = N = O = P.

The conclusions translate to:

  1. P < N(False)
  2. O < M(False)
  3. M = P(True)
Solution | Discuss! | Chapters»
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Updated on 2020-02-07. Published on: 2016-04-13

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