Inequalities Quiz Set 042

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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. ρ means X ≮ (not less than) Y
  4. ∅ means X < Y
  5. Θ means X > Y

Statements: H ∏ I; I Θ J; J ∏ K;

Conclusions:

  1. H ∅ K
  2. I ∅ 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 H ≤ I > J ≤ K. Conclusion I translates to H < K. Conclusion II translates to I < 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: N % O; O % P; P ¥ Q; Q § R;

Conclusions:

  1. Q ¥ O
  2. P ¥ R
  3. R ¥ N

Which of the above conclusions is/are true?

 A

II only.

 B

both I and II.

 C

I only.

 D

III only.

Soln.
Ans: a

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

The conclusions translate to:

  1. Q < O(False)
  2. P < R(True)
  3. R < N(False)
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. © means X < Y
  5. ∏ means X > Y

Statements: B © C; C © D; D ⊕ E; E ⊕ F;

Conclusions:

  1. F ∏ C
  2. B © D
  3. B © F

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 B < C < D = E = F.

The conclusions translate to:

  1. F > C(True)
  2. B < D(True)
  3. B < F(True)
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. η means X ≮ (not less than) Y
  4. ∇ means X < Y
  5. ∀ means X > Y

Statements: J η K; K £ L; L ∂ M;

Conclusions:

  1. J ∇ L
  2. J ∀ M
 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 J ≥ K = L ≤ M. Conclusion I translates to J < L. Conclusion II translates to J > M. 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 5

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

  1. ¢ means X = Y
  2. ⊗ means X ≯ (not more than) Y
  3. η means X ≥ Y
  4. « means X < Y
  5. Θ means X > Y

Statements: M ⊗ N; N Θ O; O η P;

Conclusions:

  1. O « M
  2. M Θ O
 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 M ≤ N > O ≥ P. Conclusion I translates to O < M. Conclusion II translates to M > O. 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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