Inequalities Quiz Set 034

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Question 1

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

  1. « means X = Y
  2. @ means X ≯ (not more than) Y
  3. ∀ means X ≮ (not less than) Y
  4. ∑ means X < Y
  5. ≅ means X > Y

Statements: D @ E; E « F; F ∑ G;

Conclusions:

  1. D ∑ G
  2. E ≅ G
 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 D ≤ E = F < G. Conclusion I translates to D < G. Conclusion II translates to E > G. 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. Δ means X = Y
  2. © means X ≤ Y
  3. ≅ means X ≥ Y
  4. « means X < Y
  5. ω means X > Y

Statements: J « K; K « L; L Δ M;

Conclusions:

  1. J « L
  2. L ω J
 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 J < K < L = M. Conclusion I translates to J < L. Conclusion II translates to L > J. 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 3

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

  1. £ means X = Y
  2. ∩ means X ≤ Y
  3. Ξ means X ≥ Y
  4. « means X < Y
  5. ∀ means X > Y

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

Conclusions:

  1. V ∀ T
  2. R ∀ U
  3. U « S

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 R > S > T < U > V.

The conclusions translate to:

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

Question 4

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: S ∇ T; T ∇ U; U @ V; V @ W;

Conclusions:

  1. S ∇ V
  2. U ∇ S
  3. W @ U

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 S > T > U < V < W.

The conclusions translate to:

  1. S > V(False)
  2. U > S(False)
  3. W < U(False)
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. λ means X ≥ Y
  4. ∀ means X < Y
  5. ω means X > Y

Statements: Q ∀ R; R ∀ S; S ω T;

Conclusions:

  1. Q ∀ T
  2. S ω 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: b

The statements can be translated to Q < R < S > T. Conclusion I translates to Q < T. Conclusion II translates to S > Q. 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»
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Updated on 2020-02-07. Published on: 2016-04-13

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