If the conditional statement

Question

“If you have a laptop, then you have a computer”

is represented by p\rightarrow q, what is the symbolic representation of

“If you have a computer, then you do not have a laptop”?

Answer 1

To represent the statement "If you have a computer, then you do not have a laptop" symbolically, we need to define our variables clearly:

• Let \( p \) represent "You have a laptop."
• Let \( q \) represent "You have a computer."

Given this, the original statement "If you have a laptop, then you have a computer" can be represented as \( p \rightarrow q \).

For the new statement "If you have a computer, then you do not have a laptop," we can express it as follows:

• "You have a computer" is simply \( q \).
• "You do not have a laptop" can be represented as \( \neg p \) (the negation of \( p \)).

Thus, the symbolic representation of the statement "If you have a computer, then you do not have a laptop" is:

\[ q \rightarrow \neg p \]