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Sagot :
Certainly, let's go through this step-by-step to understand the required condition to output "Yay!".
### Requirements:
1. The output should be "Yay!" if the integer value [tex]\( x \)[/tex] is non-negative (i.e., zero or positive).
2. Additionally, the value of [tex]\( x \)[/tex] must be even.
### Conditions Broken Down:
1. Non-negative: This condition checks if the integer is zero or positive. Mathematically, this can be represented as:
[tex]\[ x \geq 0 \][/tex]
2. Even: An integer is even if it is divisible by 2 with no remainder. In mathematical terms, this is:
[tex]\[ x \% 2 == 0 \][/tex]
Here, [tex]\( \% \)[/tex] represents the modulo operation which gives the remainder after division by 2. For an even number, this remainder is 0.
### Combined Condition:
To satisfy both the non-negative and even requirements simultaneously, we combine them using the logical AND operator which checks both conditions. In mathematical terms, this combined condition is:
[tex]\[ x \geq 0 \text{ and } x \% 2 == 0 \][/tex]
### Analysis of Given Options:
1. [tex]\( x \geq 0 \text{ and } x \% 2 == 1 \)[/tex]:
- This condition checks if [tex]\( x \)[/tex] is non-negative and odd, which contradicts the requirement for [tex]\( x \)[/tex] to be even.
2. [tex]\( x \geq 0 \text{ or } x \% 2 == 0 \)[/tex]:
- This condition will be true if either [tex]\( x \)[/tex] is non-negative or [tex]\( x \)[/tex] is even. This would be too lenient compared to our requirement (it could be satisfied by a negative even number or a non-negative odd number).
3. [tex]\( x \geq 0 \text{ and } x \% 2 == 0 \)[/tex]:
- This condition perfectly matches our requirement as it ensures [tex]\( x \)[/tex] is both non-negative and even.
4. [tex]\( x \geq 0 \text{ or } x \% 2 == 1 \)[/tex]:
- This condition will be true if either [tex]\( x \)[/tex] is non-negative or odd, which again is too lenient compared to our requirement (it could be satisfied by a non-negative odd number).
### Conclusion:
The correct condition that satisfies the requirement of outputting "Yay!" if the value is non-negative (i.e., zero or positive) and even is:
\[
x \geq 0 \text{ and } x \% 2 == 0
\
### Requirements:
1. The output should be "Yay!" if the integer value [tex]\( x \)[/tex] is non-negative (i.e., zero or positive).
2. Additionally, the value of [tex]\( x \)[/tex] must be even.
### Conditions Broken Down:
1. Non-negative: This condition checks if the integer is zero or positive. Mathematically, this can be represented as:
[tex]\[ x \geq 0 \][/tex]
2. Even: An integer is even if it is divisible by 2 with no remainder. In mathematical terms, this is:
[tex]\[ x \% 2 == 0 \][/tex]
Here, [tex]\( \% \)[/tex] represents the modulo operation which gives the remainder after division by 2. For an even number, this remainder is 0.
### Combined Condition:
To satisfy both the non-negative and even requirements simultaneously, we combine them using the logical AND operator which checks both conditions. In mathematical terms, this combined condition is:
[tex]\[ x \geq 0 \text{ and } x \% 2 == 0 \][/tex]
### Analysis of Given Options:
1. [tex]\( x \geq 0 \text{ and } x \% 2 == 1 \)[/tex]:
- This condition checks if [tex]\( x \)[/tex] is non-negative and odd, which contradicts the requirement for [tex]\( x \)[/tex] to be even.
2. [tex]\( x \geq 0 \text{ or } x \% 2 == 0 \)[/tex]:
- This condition will be true if either [tex]\( x \)[/tex] is non-negative or [tex]\( x \)[/tex] is even. This would be too lenient compared to our requirement (it could be satisfied by a negative even number or a non-negative odd number).
3. [tex]\( x \geq 0 \text{ and } x \% 2 == 0 \)[/tex]:
- This condition perfectly matches our requirement as it ensures [tex]\( x \)[/tex] is both non-negative and even.
4. [tex]\( x \geq 0 \text{ or } x \% 2 == 1 \)[/tex]:
- This condition will be true if either [tex]\( x \)[/tex] is non-negative or odd, which again is too lenient compared to our requirement (it could be satisfied by a non-negative odd number).
### Conclusion:
The correct condition that satisfies the requirement of outputting "Yay!" if the value is non-negative (i.e., zero or positive) and even is:
\[
x \geq 0 \text{ and } x \% 2 == 0
\
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