## Problem 1057

Write the statement in symbolic form. Let p and q represent the following statements.

p: The lion is fast.

q: The wildebeest is slow.

It is false that the lion is fast or the wildebeest is slow.

Solution:-

Notice that the phrase “it is false that” represents a negation that applies to the compound statement “the lion is fast or the wildebeest is slow.” When using symbols, place parentheses around the symbols that represent “ the lion is fast or the wildebeest is slow.”

Determine the proper symbol for each portion of the statement. Since the ~symbol represents negation, it is the symbol used for the first part of the statement.

It is false that   the lion is fast   or   the wildebeest is slow

~        (                                                                  )

Notice that p represents “the lion is fast.”

It is false that            the lion is fast               or      the wildebeest is slow

~                 (                  p                                              )

The symbol  v means “or.”

It is false that            the lion is fast               or      the wildebeest is slow

~                 (                            P                           v                           )

Finally, q represents “the wildebeest is slow.”

It is false that            the lion is fast     or      the wildebeest is slow

~                 (                  p                   v      q                )

Notice that the statement “It is false that” applies to the entire statement “the lion is fast or the wildebeest is slow.” Therefore , the symbolic form of the statement is  ~(p v q).