# Inequality: Exercise-1

Directions: In these questions, relationships between different elements is shown in the statements. These statements are followed by two conclusions numbered (I) and (II).

1. Statements: $$A \le F = C \le D$$, $$D \le E = B$$
Conclusions:
(I). $$B = A$$
(II). $$A \le B$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (c) If either conclusion (I) or conclusion (II) follows.

Solution: A is either smaller than or equal to B, so both the conclusions are not true.

1. Statements: $$A \lt B \lt C \lt D \gt E$$
Conclusions:
(I). $$E \lt B$$
(II). $$D \gt A$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (b) If only conclusion (II) follows.

Solution: conclusion (I) $$E \lt B$$ is not true and conclusion (II) $$D \gt A$$ is true.

1. Statements: $$P \gt Q \ge R \ge S$$, $$A \lt B = S \gt C$$
Conclusions:
(I). $$C \lt Q$$
(II). $$S \lt P$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (e) If both conclusions (I) and (II) follows.

Solution: Both the conclusions are true.

1. Statements: $$P \lt Q \lt R \lt S$$, $$R \lt T \lt U$$
Conclusions:
(I). $$U \gt P$$
(II). $$S \gt T$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (a) If only conclusion (I) follows.

Solution: conclusion (I) $$U \gt P$$ is true and conclusion (II) $$S \gt T$$ is not true.

1. Statements: $$Q \lt P \lt R$$, $$P \gt S \le T$$
Conclusions:
(I). $$Q \le T$$
(II). $$R \gt T$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (d) If neither conclusion (I) nor conclusion (II) follows.

Solution: Both the conclusions are not true.

(6-7). Statements: $$C \lt R \le E \le A = M$$, $$Y \ge E$$

1. Conclusions:
(I). $$M \ge R$$
(II). $$Y \gt A$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (a) If only conclusion (I) follows.

Solution: conclusion (I) $$M \ge R$$ is true and conclusion (II) $$Y \gt A$$ is not true.

1. Conclusions:
(I). $$C = Y$$
(II). $$C \lt Y$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (b) If only conclusion (II) follows.

Solution: conclusion (I) $$C = Y$$ is not true and conclusion (II) $$C \lt Y$$ is true.

(8-9). Statements: $$B \lt L \le A = M \ge E \ge S$$, $$L \ge W \ge J$$

1. Conclusions:
(I). $$L \lt S$$
(II). $$E \gt W$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (d) If neither conclusion (I) nor conclusion (II) follows.

Solution: Both the conclusions are not true.

1. Conclusions:
(I). $$J \lt M$$
(II). $$J = M$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (c) If either conclusion (I) or conclusion (II) follows.

Solution: J is either smaller than or equal to M, so both the conclusions are not true.

1. Statements: $$C \gt H \ge O \ge K = E \lt D$$
Conclusions:
(I). $$O \gt D$$
(II). $$E \lt C$$

1. If only conclusion (I) follows.
2. If only conclusion (II) follows.
3. If either conclusion (I) or conclusion (II) follows.
4. If neither conclusion (I) nor conclusion (II) follows.
5. If both conclusions (I) and (II) follows.

Answer: (b) If only conclusion (II) follows.

Solution: conclusion (I) $$O \gt D$$ is not true and conclusion (II) $$E \lt C$$ is true.