Inequalities Quiz Set 021

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Question 1

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

  1. Ξ means X = Y
  2. ∩ means X ≤ Y
  3. ⊗ means X ≮ (not less than) Y
  4. ≅ means X < Y
  5. ¢ means X > Y

Statements: L ∩ M; M ≅ N; N ¢ O;

Conclusions:

  1. L Ξ O
  2. L ≅ N
 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: b

The statements can be translated to L ≤ M < N > O. Conclusion I translates to L = O. Conclusion II translates to L < N. So we can see that only conclusion 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. Γ means X ≥ Y
  4. Δ means X < Y
  5. ∏ means X > Y

Statements: Q % R; R ∏ S; S Δ T; T Δ U;

Conclusions:

  1. R ∏ T
  2. S ∏ Q
  3. Q ∏ U

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 Q = R > S < T < U.

The conclusions translate to:

  1. R > T(False)
  2. S > Q(False)
  3. Q > U(False)
Solution | Discuss! | Chapters»

Question 3

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

  1. ∑ means X = Y
  2. η means X ≯ (not more than) Y
  3. @ means X ≮ (not less than) Y
  4. λ means X < Y
  5. Δ means X > Y

Statements: J @ K; K ∑ L; L @ M;

Conclusions:

  1. J ∑ L
  2. J Δ K
 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 J = L. Conclusion II translates to J > K. 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 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: M ∧ N; N © O; O © P; P ∧ Q;

Conclusions:

  1. N ∧ Q
  2. M ∧ Q
  3. M ∧ P

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 M > N = O = P > Q.

The conclusions translate to:

  1. N > Q(True)
  2. M > Q(True)
  3. M > P(True)
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. µ means X > Y

Statements: G £ H; H £ I; I ∅ J; J £ K;

Conclusions:

  1. J µ G
  2. G £ I
  3. I £ K

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 G = H = I < J = K.

The conclusions translate to:

  1. J > G(True)
  2. G = I(True)
  3. I = K(False)
Solution | Discuss! | Chapters»
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Updated on 2020-02-07. Published on: 2016-04-13

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