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Formal Logic
d. (4x)(4y)(M(x) ` W( y, x) S W( y))
e. W(i, p) ` (4x)[W( p, x) S (W(x))′])
f. (4x)[W(x, i) S (W(x))′]
27. Three forms of negation are given for each statement. Which is correct?
a. Some people like mathematics.
1. Some people dislike mathematics.
2. Everybody dislikes mathematics.
3. Everybody likes mathematics.
b. Everyone loves ice cream.
1. No one loves ice cream.
2. Everyone dislikes ice cream.
3. Someone doesn’t love ice cream.
c. All people are tall and thin.
1. Someone is short and fat.
2. No one is tall and thin.
3. Someone is short or fat.
d. Some pictures are old or faded.
1. Every picture is neither old nor faded.
2. Some pictures are not old or faded.
3. All pictures are not old or not faded.
28. Three forms of negation are given for each statement. Which is correct?
a. Nobody is perfect.
1. Everyone is imperfect.
2. Everyone is perfect.
3. Someone is perfect.
b. All swimmers are tall.
1. Some swimmer is not tall.
2. There are no tall swimmers.
3. Every swimmer is short.
c. Every planet is cold and lifeless.
1. No planet is cold and lifeless.
2. Some planet is not cold and not lifeless.
3. Some planet is not cold or not lifeless.
d. No bears are hungry.
1. Only bears are hungy.
2. All bears are hungry.
3. There is a hungry bear.
29. Write the negation of each of the following statements.
a. Some Web sites feature audio.
b. Every Web site has both audio and video.
c. Every Web site has either audio or video.