# Inequalities Quiz Set 034

### 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 ≥.

### 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 ≥.

### 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)

### 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)

### 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 ≥. This Blog Post/Article "Inequalities Quiz Set 034" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-04-13