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).