# Inequalities Quiz Set 014

### Question 1

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

1. ∀ means X = Y
2. ω means X ≯ (not more than) Y
3. « means X ≥ Y
4. ∏ means X < Y
5. Δ means X > Y

Statements: G Δ H; H ∀ I; I « J;

Conclusions:

1. H Δ J
2. H ∀ 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: d

The statements can be translated to G > H = I ≥ J. Conclusion I translates to H > J. Conclusion II translates to H = J. 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 2

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

1. ∀ means X = Y
2. @ means X ≯ (not more than) Y
3. Θ means X ≥ Y
4. § means X < Y
5. η means X > Y

Statements: M @ N; N η O; O @ P;

Conclusions:

1. M § P
2. N § O
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 M ≤ N > O ≤ P. Conclusion I translates to M < P. Conclusion II translates to N < O. 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 ≥.

### Question 3

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

1. η means X = Y
2. ≅ means X ≤ Y
3. ∅ means X ≥ Y
4. Θ means X < Y
5. ω means X > Y

Statements: O η P; P η Q; Q Θ R; R Θ S;

Conclusions:

1. P Θ R
2. S ω P
3. S ω Q

Which of the above conclusions is/are true?

A

All.

B

both I and II.

C

II only.

D

both II and III.

Soln.
Ans: a

The statements can be translated to O = P = Q < R < S.

The conclusions translate to:

1. P < R(True)
2. S > P(True)
3. S > Q(True)

### Question 4

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

1. § means X = Y
2. ω means X ≤ Y
3. % means X ≮ (not less than) Y
4. ∏ means X < Y
5. ® means X > Y

Statements: B § C; C § D; D ω E;

Conclusions:

1. B ® E
2. D ® B
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 B = C = D ≤ E. Conclusion I translates to B > E. Conclusion II translates to D > B. 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 ≥.

### 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. ≅ means X > Y

Statements: O @ P; P ∇ Q; Q ¥ R;

Conclusions:

1. O ≅ Q
2. P @ R
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 O ≥ P = Q < R. Conclusion I translates to O > Q. Conclusion II translates to P ≥ R. 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 ≥. 