## 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).

## Problem 1052

Let p and q represent the following statements.

p: Brad Pitt is not governor.

q: Jimi Hendrix is still living.

Express the following statement symbolically.

Jimi Hendrix is not still living.

Solution:-

Symbolically, the statement is ~q.

## Problem 1051

Let p and q represent the following statements.

p:  There are 33 books in the New Testament.

q: H2O is the chemical symbol for carbon dioxide.

Express the following statement symbolically.

There are not 33 books in the New Testament.

Solution:-

The negation of a statement is a statement that has a meaning that is opposite that of the original meaning.

The statement is the negation of the statement p.

The negation of a statement is expressed by writing the symbol “ ~ “ before the letter representing the statement. Therefore, the statement is expressed symbolically as ~p.