# Inequalities Quiz Set 025

### Question 1

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

1. Ξ means X = Y
2. © means X ≤ Y
3. @ means X ≥ Y
4. ∧ means X < Y
5. ∃ means X > Y

Statements: J ∧ K; K Ξ L; L ∃ M;

Conclusions:

1. J ∧ M
2. K ∃ M
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 J < K = L > M. Conclusion I translates to J < M. Conclusion II translates to K > M. 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 ≥.

### Question 2

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

1. η means X = Y
2. ¥ means X ≯ (not more than) Y
3. ⊕ means X ≥ Y
4. \$ means X < Y
5. √ means X > Y

Statements: M ⊕ N; N η O; O η P;

Conclusions:

1. M √ P
2. N η P
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 M ≥ N = O = P. Conclusion I translates to M > P. Conclusion II translates to N = P. 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. ρ means X = Y
2. § means X ≤ Y
3. ∏ means X ≥ Y
4. © means X < Y
5. ¢ means X > Y

Statements: F ρ G; G © H; H ¢ I; I ρ J;

Conclusions:

1. I ¢ G
3. H ρ J

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 F = G < H > I = J.

The conclusions translate to:

1. I > G(False)
2. F < J(False)
3. H = J(False)

### Question 4

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. Θ means X < Y
5. ≅ means X > Y

Statements: B \$ C; C £ D; D ∧ E;

Conclusions:

1. C ≅ E
2. D £ 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: d

The statements can be translated to B ≤ C = D ≥ E. Conclusion I translates to C > E. Conclusion II translates to D = E. So we can see that either I or II can be true.

Please remember that in such questions ≯ (not more than) is same as ≤, and ≮ (not less than) is same as ≥.

### 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. ∏ means X ≮ (not less than) Y
4. @ means X < Y
5. Γ means X > Y

Statements: N @ O; O Γ P; P @ Q;

Conclusions:

1. N @ O
2. O @ 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: c

The statements can be translated to N < O > P < Q. Conclusion I translates to N < O. Conclusion II translates to O < Q. 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 ≥. 