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17. If Anne comes home early, then either Barry makes pasta or Carrie takes everyone out to sushi. (a) a V (b V c) (b) a -> (b -> c) (c) a -> (b V c) (d) a <-> (b V c) 18. Unless Anne comes home early, both Barry will make pasta and Donald will go hungry. (a) ~a -> (b & d) (b) (b & d) -> a (c) ~a -> ~(b & d) (d) a & (b -> d) 19. Barry makes pasta only if both Anne comes home early and Carrie doesn't take everyone out to sushi. (a) b <-> (a & c) (b) b -> (a & ~c) (c) (a & ~c) -> b (d) (b -> a) & ~c 20. Barry will make pasta if Anne doesn't come home early; but if Anne comes home early, then both Carrie will take everyone out to sushi and Donald won't go hungry. (a) (b -> ~a) & ((a -> c) & d) (b) (~a -> b) -> ((a -> c) & ~d) (c) (~a -> b) & ((c & ~d) -> a) (d) (~a -> b) & (a -> (c & ~d))

          17. If Anne comes home early, then either Barry makes pasta or Carrie takes everyone out to sushi.
(a) a V (b V c)
(b) a -> (b -> c)
(c) a -> (b V c)
(d) a <-> (b V c)

18. Unless Anne comes home early, both Barry will make pasta and Donald will go hungry.
(a) ~a -> (b & d)
(b) (b & d) -> a
(c) ~a -> ~(b & d)
(d) a & (b -> d)

19. Barry makes pasta only if both Anne comes home early and Carrie doesn't take everyone out to sushi.
(a) b <-> (a & c)
(b) b -> (a & ~c)
(c) (a & ~c) -> b
(d) (b -> a) & ~c

20. Barry will make pasta if Anne doesn't come home early; but if Anne comes home early, then both Carrie will take everyone out to sushi and Donald won't go hungry.
(a) (b -> ~a) & ((a -> c) & d)
(b) (~a -> b) -> ((a -> c) & ~d)
(c) (~a -> b) & ((c & ~d) -> a)
(d) (~a -> b) & (a -> (c & ~d))

17. If Anne comes home early, then either Barry makes pasta or Carrie takes everyone out to sushi.
(a) a V (b V c)
(b) a -> (b -> c)
(c) a -> (b V c)
(d) a <-> (b V c)

18. Unless Anne comes home early, both Barry will make pasta and Donald will go hungry.
(a) a -> (b d)
(b) (b d) -> a
(c) a -> (b d)
(d) a (b -> d)

19. Barry makes pasta only if both Anne comes home early and Carrie doesn't take everyone out to sushi.
(a) b <-> (a c)
(b) b -> (a c)
(c) (a c) -> b
(d) (b -> a) c

20. Barry will make pasta if Anne doesn't come home early; but if Anne comes home early, then both Carrie will take everyone out to sushi and Donald won't go hungry.
(a) (b -> a) ((a -> c) d)
(b) ( a -> b) -> ((a -> c) d)
(c) ( a -> b) ((c d) -> a)
(d) ( a -> b) (a -> (c d))

Added by Antonio R.

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