Truth Tables and De Morgan's Rules
16. Free Shipping
Answer:
Using the De Morgan Rule
!(A && B)
is equivalent to!A && !B
the expression
boolean oilOK = !( months >= 3 || miles >= 3000 );is equivalent to
boolean oilOK = !( months >= 3 ) && !( miles >= 3000 );which can be further transformed to
boolean oilOK = ( months < 3 ) && ( miles < 3000 );
Free Shipping
For an on-line shopping site, shipping is free for purchases of $50 or more, unless the merchandise is on sale.
boolean freeShipping = purchase >= 50 && !onSale;
Here is an expression that shows when to charge for shipping:
boolean shipping = !( purchase >= 50 && !onSale );
Assume that onSale
is a boolean variable.
Question 16:
Rewrite the second expression in two steps. In the first step, apply De Morgan's rule that
!(A && B)
is equivalent to!(A) || !(B)
.boolean shipping =
In the second step, rewrite the relational expression:
boolean shipping =