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In a certain code, 'A @ B' means A is not smaller than B; 'A # B' means A is not greater than B; and 'A $ B' means A is neither smaller than nor equal to B. Given the statements 'P @ Q' and 'Q $ R' are true, consider the conclusions: I. P $ R
II. P @ R. Which conclusion(s) is/are true?

Competition practiceInequalities
  • AOnly I is true
  • BBoth I and II are true
  • COnly II is true
  • DNeither I nor II is true

Step-by-Step Solution

P @ Q means P >= Q and Q $ R means Q > R, so P >= Q > R gives P > R. Then P $ R (P > R) is true, and P @ R (P >= R) is also true.
Answer: B) Both I and II are true

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