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In a coded language: 'P & Q' means P > Q and 'P $ Q' means P = Q, while 'P @ Q' means P ≥ Q and 'P © Q' means P < Q. Given that 'A $ B' and 'B @ C' are both true, which of the following is definitely true?

Competition practiceInequalities
  • AA $ C is definitely true
  • BA & C is definitely true
  • CEither 'A & C' or 'A $ C' is true
  • DA © C is definitely true

Step-by-Step Solution

'A $ B' is A = B and 'B @ C' is B ≥ C, so A = B ≥ C gives A ≥ C, i.e. A > C or A = C. Hence either 'A & C' or 'A $ C' must hold.
Answer: C) Either 'A & C' or 'A $ C' is true

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