  Question

# In the following questions, the symbols $,%,@,© and ∗ are used with the following meaning as illustrated below. ‘P%Q′ means 'P is neither greater than nor smaller than Q'. ′P$Q′ means 'P is neither smaller than nor equal to Q'. ‘P©Q′ means `P is neither greater than nor equal to Q'. P∗Q′ means 'P is not greater than Q'. ′P@Q′ means 'P is not smaller than Q'. Now, in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is/are definitely true and give your answer accordingly. %⇒=,@⇒≥,$⇒>,©⇒<,∗⇒≤ Statements K@T;T$N;N©R Conclusions I. R$K II. N∗K III. K$NAll are trueNone is trueOnly II is trueOnly I is trueOnly III is true

Solution

## The correct option is E Only III is trueGiven statements are K@N⇒K≥T       ...(i) T$N⇒T>N ...(ii) N©R⇒N<R ...(iii) From all above statements, we get K≥T>N<R I. R$K⇒R>K       (False) As, relation cannot be established II. N∗K⇒N≤K   (False) As, K≥T>N So, K > N III. K\$N⇒K>N (True) As, K≥T>N So, K > N  Suggest corrections   