Inequalities Quiz Set 033

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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: F © G; G ∧ H; H ∧ I;

Conclusions:

  1. F © I
  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: a

The statements can be translated to F < G = H = I. Conclusion I translates to F < I. Conclusion II translates to G = I. 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 2

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

  1. ¢ means X = Y
  2. « means X ≤ Y
  3. ∀ means X ≥ Y
  4. λ means X < Y
  5. © means X > Y

Statements: R © S; S © T; T © U; U λ V;

Conclusions:

  1. R © U
  2. S © U
  3. V λ R

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

Question 3

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

  1. Θ means X = Y
  2. Ω means X ≯ (not more than) Y
  3. $ means X ≮ (not less than) Y
  4. « means X < Y
  5. η means X > Y

Statements: F Θ G; G « H; H η I;

Conclusions:

  1. F Θ I
  2. H η 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: b

The statements can be translated to F = G < H > I. Conclusion I translates to F = I. Conclusion II translates to H > F. 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. Ξ means X < Y
  5. ⊕ means X > Y

Statements: L ⊕ M; M λ N; N λ O; O ⊕ P;

Conclusions:

  1. N Ξ P
  2. O Ξ L
  3. O Ξ M

Which of the above conclusions is/are true?

 A

both II and III.

 B

I only.

 C

II only.

 D

III only.

Soln.
Ans: a

The statements can be translated to L > M = N = O > P.

The conclusions translate to:

  1. N < P(False)
  2. O < L(True)
  3. O < M(True)
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. Ω means X ≥ Y
  4. © means X < Y
  5. ∇ means X > Y

Statements: R ∇ S; S © T; T © U; U Γ V;

Conclusions:

  1. T Γ V
  2. R © U
  3. T © R

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. T = V(False)
  2. R < U(False)
  3. T < R(False)
Solution | Discuss! | Chapters»
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Updated on 2020-02-07. Published on: 2016-04-13

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