Let game(ball, rugby) be true if the ball is used in rugby and false…

To determine which logical sentences represent the assertion "All balls are round except balls used in rugby", we analyze the meaning of the statement. The assertion means: all balls that are not used in rugby are round, and all balls used in rugby are not round. Now, evaluate each sentence: s1: ∀ball ¬game(ball, rugby) ⟹ shape(ball, round) — This means: if a ball is not used in rugby, then it is round. This matches the first part of the assertion. s2: ∀ball ¬shape(ball, round) ⟹ game(ball, rugby) — This means: if a ball is not round, then it is used in rugby. This is not equivalent to the assertion, as it allows non-round balls to be used in rugby but does not exclude round balls from being used in rugby. s3: ∀ball game(ball, rugby) ⟹ ¬shape(ball, round) — This means: if a ball is used in rugby, then it is not round. This matches the second part of the assertion. s4: ∀ball shape(ball, round) ⟹ ¬game(ball, rugby) — This means: if a ball is round, then it is not used in rugby. This is equivalent to s1 and supports the idea that non-rugby balls are round. Now, evaluate the options: A: s1 ∧ s3 — This combines: if not used in rugby, then round (s1), and if used in rugby, then not round (s3). This fully captures the assertion. B: s1 ∧ s2 — s1 is correct, but s2 allows non-round balls to be used in rugby and does not prevent round balls from being used in rugby. This is incorrect. C: s2 ∧ s3 — s3 is correct, but s2 does not ensure that all non-rugby balls are round. This is incomplete. D: s3 ∧ s4 — s3 is correct, and s4 implies that round balls are not used in rugby, which is equivalent to s1. However, s4 is not necessary, and the combination does not fully capture the intended meaning as clearly as s1 ∧ s3. Therefore, the correct choice is A: s1 ∧ s3.