Inequalities Quiz Set 046

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Question 1

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

  1. ∑ means X = Y
  2. Ω means X ≤ Y
  3. ® means X ≮ (not less than) Y
  4. Θ means X < Y
  5. @ means X > Y

Statements: L Ω M; M Θ N; N Θ O;

Conclusions:

  1. L Θ O
  2. N ∑ 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 L ≤ M < N < O. Conclusion I translates to L < O. Conclusion II translates to N = 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 2

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

  1. Θ means X = Y
  2. Γ means X ≤ Y
  3. ∇ means X ≮ (not less than) Y
  4. « means X < Y
  5. √ means X > Y

Statements: R Θ S; S « T; T √ U;

Conclusions:

  1. R Θ U
  2. T √ R
 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 R = S < T > U. Conclusion I translates to R = U. Conclusion II translates to T > R. 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 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. Ξ means X < Y
  5. ∏ means X > Y

Statements: Q Ξ R; R Ξ S; S ⊕ T; T ∏ U;

Conclusions:

  1. R Ξ U
  2. R Ξ T
  3. Q Ξ S

Which of the above conclusions is/are true?

 A

both II and III.

 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 < U(False)
  2. R < T(True)
  3. Q < S(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. Ω means X < Y
  5. $ means X > Y

Statements: F ∑ G; G Ω H; H $ I; I Ω J;

Conclusions:

  1. F Ω J
  2. I $ F
  3. J Ω 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 F = G < H > I < J.

The conclusions translate to:

  1. F < J(False)
  2. I > F(False)
  3. J < H(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. Ω means X ≥ Y
  4. § means X < Y
  5. @ means X > Y

Statements: G @ H; H @ I; I § J; J § K;

Conclusions:

  1. G @ K
  2. H @ J
  3. H @ 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 G > H > I < J < K.

The conclusions translate to:

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

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