# Inequalities Quiz Set 003

### 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 ≥ Y
4. ∅ means X < Y
5. ∃ means X > Y

Statements: M ≅ N; N ∃ O; O ∃ P;

Conclusions:

1. M √ P
2. N ∃ 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: b

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 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. Ξ means X = Y
2. ∩ means X ≤ Y
3. ⊗ means X ≮ (not less than) Y
4. ≅ means X < Y
5. ¢ means X > Y

Statements: L ∩ M; M ≅ N; N ¢ O;

Conclusions:

1. L Ξ O
2. L ≅ N
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 L ≤ M < N > O. Conclusion I translates to L = O. Conclusion II translates to L < N. 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 3

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

1. ∩ means X = Y
2. ≅ means X ≤ Y
3. ¢ means X ≥ Y
4. η means X < Y
5. ∏ means X > Y

Statements: I η J; J ∏ K; K η L;

Conclusions:

1. I η J
2. J η L
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 I < J > K < L. Conclusion I translates to I < J. Conclusion II translates to J < L. 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 4

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: L ∇ M; M ∇ N; N @ O; O @ P;

Conclusions:

1. M ∇ O
2. L ∇ O
3. P ∇ N

Which of the above conclusions is/are true?

A

III only.

B

both III and II.

C

II only.

D

I only.

Soln.
Ans: a

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

The conclusions translate to:

1. M > O(False)
2. L > O(False)
3. P > N(True)

### Question 5

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)