(De Morgan's Latus) In this chapter, we discussed the logical operators \(\&
\&, \&,||, |, \wedge\) and \(!\) De Morgan's laws can sometimes make it more
convenient for us to express a logical expression. These laws state that the
expression ! (condition1 \&\& condition2) is logically equivalent to the
expression \((| \text { condition } I|| \text { I condition2). Also, the
expression } ! \text { (condition } I\) | | condition2) is logically equivalent
to the expression ( 1 condition 1 \&\& I condition2). Use De Morgan's laws to
write equivalent expressions for each of the following, then write an
application to show that both the original expression and the new expression
in each case produce the same value:
a) !( x < 5 ) && !( y >= 7 )
b) !( a == b ) || !( g != 5 )
c) !( ( x <= 8 ) && ( y > 4 ) )
d) !( ( i > 4 ) || ( j <= 6 ) )