0
  1. Not all three balls are of the same colour. (Colours are black or white.)
  2. Among the three balls, there is exactly one white ball, or there is exactly one black ball.

I know they are are logically equivalent. However, i don't know how to formulate them using logical symbols.

Any helps please?

game game
  • 21
  • 2
  • Are you sure that you have to use propositional calculus ? – Mauro ALLEGRANZA Sep 14 '17 at 05:58
  • If you want to symbolize them with prop calculus, you can use three prop variavles $B_i$ meaning: "ball $i$ is Black". In this way, $\lnot B_i$ reads: "ball $i$ is not-Black, i.e. White". – Mauro ALLEGRANZA Sep 14 '17 at 07:03
  • In this way, we can symbolize 1) as follows: $\lnot (B_1 \land B_2 \land B_3) \land \lnot (\lnot B_1 \land \lnot B_2 \land \lnot B_3)$ or equivalently: $(\lnot B_1 \lor \lnot B_2 \lor \lnot B_3) \land (B_1 \lor B_2 \lor B_3)$. – Mauro ALLEGRANZA Sep 14 '17 at 07:05

0 Answers0