To determine the relationship between the two statements:
1. First Statement:
[tex]\[
x = y
\][/tex]
2. Second Statement:
[tex]\[
7x = 75
\][/tex]
Step-by-Step Solution:
1. From the first statement, we know that [tex]\( x \)[/tex] equals [tex]\( y \)[/tex]:
[tex]\[
x = y
\][/tex]
2. Substitute [tex]\( x \)[/tex] with [tex]\( y \)[/tex] in the second statement:
[tex]\[
7x = 75 \implies 7y = 75
\][/tex]
3. Solve the second statement for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{75}{7}
\][/tex]
Calculate the integer part of [tex]\( \frac{75}{7} \)[/tex]:
[tex]\[
y \approx 10.71 \quad \text{(This gives approximate value, but we will go with the integer part here.)}
\][/tex]
Integer part of [tex]\( \frac{75}{7} \)[/tex] is [tex]\( 10 \)[/tex].
4. The integer part of [tex]\( \frac{75}{7} \)[/tex] is [tex]\( 10 \)[/tex], indicating:
[tex]\[
y \approx 10
\][/tex]
5. Since [tex]\( x = y \)[/tex], substitute back:
[tex]\[
x \approx 10
\][/tex]
Comparing the statements:
- First statement implies [tex]\( x = y \)[/tex].
- Second statement, when solved, provides [tex]\( x \approx 10 \)[/tex].
Since the second statement provides a specific value for [tex]\( x \)[/tex] that was derived from the relationship [tex]\( 7x = 75 \)[/tex], and does not align directly with [tex]\( x = y \)[/tex] without specific values, it represents a conflicting, mutually exclusive relationship with the first statement.
Thus, we can conclude that the second statement is a contradiction of the first.
Answer:
B. Contradiction
