What is the conditional statement of the sentence?
For all real numbers a, b, and c, a = b implies that a−c=b−c.
A. If a, b, and c are real numbers, then a = b.
B. For all real numbers a, b, and c, if a = b, then a−c=b−c.
C. For all real numbers a, b, and c, if a−c=b−c, then a = b.
D. If a, b, and c are real numbers, then a−c=b−c.
The conditional statement is the implication or if-then statement in the sentence. It states that "a = b implies that a - c = b - c."
To identify the conditional statement, we look for the "if-then" structure. In this case, the structure is "a = b implies that a - c = b - c."
By examining the options provided:
A. "If a, b, and c are real numbers, then a = b": This option does not match the given conditional statement because it does not mention the implication related to a - c and b - c.
B. "For all real numbers a, b, and c, if a = b, then a - c = b - c": This option accurately represents the given conditional statement in the correct "if-then" structure.
C. "For all real numbers a, b, and c, if a - c = b - c, then a = b": This option reverses the conditional statement in the original sentence, stating that if a - c = b - c, then a = b. It does not align with the original conditional statement.
D. "If a, b, and c are real numbers, then a - c = b - c": This option again does not include the "if-then" structure regarding a and b.
Therefore, the correct answer is option B - "For all real numbers a, b, and c, if a = b, then a - c = b - c."