Inequalities Quiz Set 009

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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: R £ S; S ∧ T; T ∧ U; U ∧ V;

Conclusions:

  1. R £ V
  2. R § T
  3. S ∧ V

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 R < S = T = U = V.

The conclusions translate to:

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

Question 2

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

  1. © means X = Y
  2. ∃ means X ≯ (not more than) Y
  3. Ξ means X ≮ (not less than) Y
  4. ρ means X < Y
  5. Θ means X > Y

Statements: Q Θ R; R © S; S ∃ T;

Conclusions:

  1. Q ρ T
  2. S Θ Q
 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 Q > R = S ≤ T. Conclusion I translates to Q < T. Conclusion II translates to S > Q. 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 3

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

  1. Δ means X = Y
  2. ® means X ≤ Y
  3. © means X ≮ (not less than) Y
  4. ∂ means X < Y
  5. « means X > Y

Statements: B Δ C; C Δ D; D « E;

Conclusions:

  1. B Δ E
  2. C « E
 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 B = C = D > E. Conclusion I translates to B = E. Conclusion II translates to C > E. 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»

Question 4

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

  1. λ means X = Y
  2. ∩ means X ≤ Y
  3. % means X ≥ Y
  4. $ means X < Y
  5. Ξ means X > Y

Statements: B λ C; C $ D; D $ E;

Conclusions:

  1. B $ D
  2. C Ξ E
 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 B = C < D < E. Conclusion I translates to B < D. Conclusion II translates to C > E. 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. Γ means X = Y
  2. ∧ means X ≤ Y
  3. λ means X ≥ Y
  4. § means X < Y
  5. ∃ means X > Y

Statements: D § E; E Γ F; F § G; G § H;

Conclusions:

  1. E § G
  2. D § H
  3. F § D

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 D < E = F < G < H.

The conclusions translate to:

  1. E < G(True)
  2. D < H(True)
  3. F < D(False)
Solution | Discuss! | Chapters»
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Updated on 2020-02-07. Published on: 2016-04-13

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