# Ineqality

Directions (Q 1–4): In the questions given below, certain symbols are used with the following meanings:

P \$ Q means P is neither equal to nor smaller than Q.
P © Q means P is not smaller than Q.
P « Q means P is neither greater nor smaller than Q.
P # Q means P is neither greater than nor equal to Q.
P @ Q means P is not greater than Q.

Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true. Give answer
1) if only conclusion I is true.
2) if only conclusion II is true.
3) if either conclusion I or II is true.
4) if neither conclusion I nor II is true.

5) if both conclusions I and II are true.

1. Statements: M # K, K « D, D @ P
Conclusions: I. M @ P II. M «P

2. Statements: I. W © T, T \$ M, B # M
Conclusions: I. W \$ B II. M # W

3. Statements: H « D, D # R, R © N
Conclusions: I. N « H II. N \$ H

4. Statements: Z @ R, R © D, D # T
Conclusions: I. D # Z II. Z # T

Answers
1. 4; M < K ... (i); K = D... (ii); D ? P... (iii) Combining all the equations, we get P ? D = K > M ? P > M. Hence, conclusion I (M ? P) and conclusion II (M = P) are not true.

2. 5; W ? T ... (i); T > M ... (ii); B < M ... (iii) Combining all, we get W ? T > M > B ? W > B and W > M. Hence, both conclusions
(W > B, M < W) are true.

3. 4; H = D ... (i); D < R ... (ii) R ? N .... (iii) Combining (i) and (ii), we get R > H = D ... (iv)
From (iii) and (iv), we cann’t get any specific relation between N and H. Therefore, conclusion I (N = H) and conclusion II (N > H) are not true.

4. 4; Z ? R ... (i); R ??D ... (ii); D < T... (iii) With these equations no relation can be established between D and Z, and Z and T.

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