Inequalities Quiz Set 026

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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. Δ means X ≥ Y
  4. √ means X < Y
  5. Γ means X > Y

Statements: S η T; T √ U; U η V;

Conclusions:

  1. S Γ U
  2. V √ S
 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 S ≤ T < U ≤ V. Conclusion I translates to S > U. Conclusion II translates to V < S. 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. Ω means X ≤ Y
  3. ∃ means X ≥ Y
  4. η means X < Y
  5. ⊕ means X > Y

Statements: N ⊕ O; O ⊕ P; P η Q; Q η R;

Conclusions:

  1. N ⊕ R
  2. O η R
  3. O ⊕ Q

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 N > O > P < Q < R.

The conclusions translate to:

  1. N > R(False)
  2. O < R(False)
  3. O > Q(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. Θ means X > Y

Statements: F ∧ G; G ⊕ H; H ∧ I; I ∧ J;

Conclusions:

  1. J ⊕ H
  2. F ⊕ J
  3. G ⊕ I

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 F = G < H = I = J.

The conclusions translate to:

  1. J < H(True)
  2. F < J(True)
  3. G < I(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. ρ means X ≥ Y
  4. £ means X < Y
  5. © means X > Y

Statements: M $ N; N © O; O £ P;

Conclusions:

  1. O £ P
  2. O £ 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: c

The statements can be translated to M ≤ N > O < P. Conclusion I translates to O < P. Conclusion II translates to O < M. 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 5

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. √ means X < Y
  5. © means X > Y

Statements: F √ G; G ⊗ H; H √ I;

Conclusions:

  1. F √ H
  2. G ∀ I
 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 F < G = H < I. Conclusion I translates to F < H. Conclusion II translates to G ≥ I. 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»
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Updated on 2020-02-07. Published on: 2016-04-13

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