'P @ Q' means 'P is not smaller than Q'.
'P # Q' means 'P is neither greater than nor equal to Q'.
'P $ Q' means 'P is neither smaller than nor greater than Q'.
'P ⋆ Q' means 'P is not greater than Q'.
'P % Q' means 'P is neither smaller than nor equal to 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.
Give answer (2) if only Conclusion II is true.
Give answer (3) if either Conclusion I or II is true.
Give answer (4) if neither Conclusion I nor II is true.
Give answer (5) if both Conclusions I and II are true.
Statements : M $ K, D ✬ K, R # K$
Conclusions : I. D $ M II. M % D
Correct Answer: (3)
Solution:(i) P @ Q ⟹ P ≥ QTherefore, P > Q or P = Q
Thus, P ≥ Q
(ii) P # Q ⟹ P î€ = Q and P î€ = Q
Therefore, P < Q
(iii) P S Q ⟹ P î€ = Q and P î€ = Q
Therefore, P = Q
(iv) P ∗ Q ⟹ P î€ = Q
Therefore, P < Q and P = Q
Thus, P ≤ Q
(v) P % Q ⟹ P î€ = Q and P î€ = Q
Therefore, P > Q
Statements
M S K ⟹ M = K
D ∗ K ⟹ D ≤ K
R # K ⟹ R < K
Therefore, R < M = K ≥ D
