Inequalities Set 12

Directions (1-5) In the following questions, the symbols @, $, %, # and © are used with the following meanings illustrated—

(i) ‘X @ Y’ means ‘X is not smaller than Y’.
(ii) ‘X $ Y’ means ‘X is not greater than Y’.
(iii) ‘X % Y’ means ‘X is neither smaller than nor equal to Y’.
(iv) ‘X # Y’ means ‘X is neither greater than nor equal to Y’.
(v) ‘X © Y’ means ‘X is neither smaller than nor greater than Y’.
In each of the following questions assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true. Give answer—
(a)If only I is true.
(b)If only II is true.
(c)If either I or II is true
(d)If neither I nor II is true.
(e)If both I and II are true.
Q1. Statements: P $ T, T @ L, U % L
Conclusions: I. P @ L II. U©L
Q2. Statements: A @B, B%D, D©K
Conclusions: I. A©K II. B%K
Q3. Statements: J # K, K©L, P$L
Conclusions: I. P$K II. J#L
Q4. Statements: T % O, T # M, [email protected] V
Conclusions: I. M % T II. O % V
Q5. Statements: K @ T, T # C, C $ P
Conclusions: I. C © K II. C % K


1. Ans.(d)

Sol. Statement-P≤T≥L

Conclusion- P≥L, U=L
2. Ans.(b)
Sol. Statement- A≥B>D=K
Conclusion- A=K, B>K
3. Ans.(e)

Sol. Statement- J

Conclusion- P≤K, J

4. Ans.(a)
Sol. Statement- V≤M>T>O
5. Ans.(d)

Sol. Statement- K≥T

Conclusion- C=K, C>K

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