Inequalities Quiz Set 017

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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. $ means X ≥ Y
  4. ∂ means X < Y
  5. ∧ means X > Y

Statements: S ∂ T; T ∂ U; U ∧ V; V « W;

Conclusions:

  1. U ∧ S
  2. S ∂ V
  3. S ∂ W

Which of the above conclusions is/are true?

 A

I only.

 B

both I and II.

 C

II only.

 D

III only.

Soln.
Ans: a

The statements can be translated to S < T < U > V = W.

The conclusions translate to:

  1. U > S(True)
  2. S < V(False)
  3. S < W(False)
Solution | Discuss! | Chapters»

Question 2

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

  1. µ means X = Y
  2. $ means X ≤ Y
  3. ® means X ≥ Y
  4. % means X < Y
  5. ∀ means X > Y

Statements: R µ S; S µ T; T ∀ U; U ∀ V;

Conclusions:

  1. R µ T
  2. U % S
  3. R ∀ V

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 R = S = T > U > V.

The conclusions translate to:

  1. R = T(True)
  2. U < S(True)
  3. R > V(False)
Solution | Discuss! | Chapters»

Question 3

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

  1. Θ means X = Y
  2. ≅ means X ≯ (not more than) Y
  3. Ξ means X ≥ Y
  4. ∃ means X < Y
  5. Δ means X > Y

Statements: N Θ O; O Θ P; P Θ Q;

Conclusions:

  1. N Θ P
  2. P Θ Q
 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: a

The statements can be translated to N = O = P = Q. Conclusion I translates to N = P. Conclusion II translates to P = Q. So we can see that both I and II are 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. η means X > Y

Statements: C ¥ D; D η E; E ¢ F;

Conclusions:

  1. E η F
  2. E £ F
 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 C < D > E ≥ F. Conclusion I translates to E > F. Conclusion II translates to E = F. 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 5

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

  1. ⊕ means X = Y
  2. √ means X ≤ Y
  3. η means X ≥ Y
  4. @ means X < Y
  5. Θ means X > Y

Statements: Q @ R; R ⊕ S; S @ T; T @ U;

Conclusions:

  1. R @ U
  2. S Θ U
  3. R @ T

Which of the above conclusions is/are true?

 A

both I 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(True)
  2. S > U(False)
  3. R < T(True)
Solution | Discuss! | Chapters»
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Updated on 2020-02-07. Published on: 2016-04-13

Posted by Parveen(Hoven),
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