Inequalities Quiz Set 045

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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. ρ means X < Y
  5. µ means X > Y

Statements: O µ P; P µ Q; Q « R; R « S;

Conclusions:

  1. S ρ P
  2. O ρ Q
  3. O µ S

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 O > P > Q = R = S.

The conclusions translate to:

  1. S < P(True)
  2. O < Q(False)
  3. O > S(True)
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 ≮ (not less than) Y
  4. ρ means X < Y
  5. Ω means X > Y

Statements: Q © R; R ρ S; S ρ T;

Conclusions:

  1. T Ω R
  2. R © T
 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 Q ≥ R < S < T. Conclusion I translates to T > R. Conclusion II translates to R ≥ T. 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 3

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

  1. ¥ means X = Y
  2. ρ means X ≤ Y
  3. $ means X ≮ (not less than) Y
  4. η means X < Y
  5. © means X > Y

Statements: R ¥ S; S © T; T η U;

Conclusions:

  1. R © T
  2. T η U
 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 R = S > T < U. Conclusion I translates to R > T. Conclusion II translates to T < U. 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 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. ω means X > Y

Statements: M ω N; N ω O; O √ P; P √ Q;

Conclusions:

  1. N √ Q
  2. Q ω O
  3. O ω M

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 M > N > O < P < Q.

The conclusions translate to:

  1. N < Q(False)
  2. Q > O(True)
  3. O > M(False)
Solution | Discuss! | Chapters»

Question 5

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

  1. √ means X = Y
  2. λ means X ≤ Y
  3. $ means X ≮ (not less than) Y
  4. ∇ means X < Y
  5. ⊕ means X > Y

Statements: M √ N; N ⊕ O; O λ P;

Conclusions:

  1. M ⊕ P
  2. O ∇ 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 M = N > O ≤ P. Conclusion I translates to M > P. Conclusion II translates to O < 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»
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Updated on 2020-02-07. Published on: 2016-04-13

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