Inequalities Quiz Set 037

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Question 1

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

  1. √ means X = Y
  2. η means X ≤ Y
  3. Γ means X ≥ Y
  4. £ means X < Y
  5. ¢ means X > Y

Statements: H √ I; I £ J; J ¢ K; K ¢ L;

Conclusions:

  1. I ¢ L
  2. H £ L
  3. I £ K

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 H = I < J > K > L.

The conclusions translate to:

  1. I > L(False)
  2. H < L(False)
  3. I < K(False)
Solution | Discuss! | Chapters»

Question 2

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. Ω means X > Y

Statements: F ® G; G ∏ H; H £ I;

Conclusions:

  1. F Ω I
  2. H ∏ F
 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 F = G < H ≤ I. Conclusion I translates to F > I. Conclusion II translates to H < F. 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. ω means X ≥ Y
  4. % means X < Y
  5. Δ means X > Y

Statements: C % D; D % E; E ∏ F; F ∏ G;

Conclusions:

  1. C % E
  2. F Δ C
  3. D % G

Which of the above conclusions is/are true?

 A

All.

 B

both I and II.

 C

II only.

 D

both II and III.

Soln.
Ans: a

The statements can be translated to C < D < E = F = G.

The conclusions translate to:

  1. C < E(True)
  2. F > C(True)
  3. D < G(True)
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: B ∩ C; C ∂ D; D ∩ E; E ∩ F;

Conclusions:

  1. D ∂ B
  2. B ∩ F
  3. E ∩ C

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 B > C < D > E > F.

The conclusions translate to:

  1. D < B(False)
  2. B > F(False)
  3. E > C(False)
Solution | Discuss! | Chapters»

Question 5

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;

Conclusions:

  1. K √ M
  2. K ∅ M
 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 J < K = L ≥ M. Conclusion I translates to K > M. Conclusion II translates to K = M. 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»
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Updated on 2020-02-07. Published on: 2016-04-13

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