In the question the symbols @, #, %, $ and H are used with the following…
2025
In the question the symbols @, #, %, $ and H are used with the following meaning :
‘P $ Q’ means ‘P is smaller than Q’
‘P @ Q’ means P is neither greater than nor equal to Q’
‘P H Q’ means ‘P is neither smaller than nor equal to Q’
‘P % Q’ means ‘P is not greater than Q’
‘P # Q’ means ‘P is neither greater than nor smaller than Q’
Now assume the given statements to be true and find which
out of the two conclusions I and II is/are definitely true.
Statements:
J % N, K @ N, T $ K
Conclusions:
I.T H J
II. J @ K
- A.
Only conclusion I is true
- B.
Only conclusion II is true
- C.
Either conclusion I or II is true
- D.
Neither conclusion I nor II is true
Attempted by 21 students.
Show answer & explanation
Correct answer: D
Symbol meanings:
P $ Q means P < Q (P is smaller than Q).
P @ Q means P < Q (P is neither greater than nor equal to Q).
P H Q means P > Q (P is neither smaller than nor equal to Q).
P % Q means P ≤ Q (P is not greater than Q).
P # Q means P = Q (P is neither greater than nor smaller than Q).
Translate the given statements:
J % N ⇒ J ≤ N
K @ N ⇒ K < N
T $ K ⇒ T < K
Reasoning and counterexamples:
From T < K and K < N we deduce T < K < N, so T < N.
Since J ≤ N, J may equal N or be less than N. The relation between J and K is not fixed by these statements.
Counterexample showing the first conclusion is not definitely true: choose N = 10, K = 9, T = 8, J = 10. Then T < K < N and J = N, so T < J (not T > J).
Counterexample showing the second conclusion is not definitely true: with the same values (J = N = 10, K = 9), J > K, so J < K is false.
Conclusion: Neither conclusion I (T H J, meaning T > J) nor conclusion II (J @ K, meaning J < K) is definitely true based on the given statements.