Question

Of the following choices, which expression is !(x < y || z != 9) equivalent to?
Group of answer choices

x > y || z == 9

x > y && z == 9

x >= y || z == 9

x >= y && z == 9

x > y && z != 9

Answer 1

To determine which expression is equivalent to \( !(x < y || z \neq 9) \), we can apply De Morgan's laws. According to De Morgan's laws, the negation of a disjunction (OR statement) can be rewritten as a conjunction (AND statement) of the negations.

Given:
\[ !(x < y || z \neq 9) \]

We can apply De Morgan's law:

1. Negate both conditions inside the parentheses:
\[ !(x < y) \text{ and } !(z \neq 9) \]

2. Negating the first condition \( !(x < y) \) gives us:
\[ x \geq y \]
(because if \( x < y \) is false, then \( x \) must be greater than or equal to \( y \))

3. Negating the second condition \( !(z \neq 9) \) gives us:
\[ z == 9 \]
(because if \( z \neq 9 \) is false, then \( z \) must equal 9)

Putting it all together:
\[ !(x < y || z \neq 9) \] is equivalent to:
\[ x \geq y \text{ and } z == 9 \]

So the expression you are looking for is:
**\( x \geq y && z == 9 \)**.