QuestionCreate a new conditional statement using the Law of Syllogism from these true statements:
1. If a figure is a rhombus, then it is a parallelogram.
2. If a figure is a parallelogram, then it has two pairs of parallel sides.
Studdy Solution
STEP 1
Assumptions1. The first statement is If a figure is a rhombus, then the figure is a parallelogram.
. The second statement is If a figure is a parallelogram, then the figure has two pairs of opposite sides that are parallel.
3. The Law ofyllogism states that if "if p then q" and "if q then r" are true statements, then "if p then r" is a true statement.
STEP 2
Identify the p, q, and r in the given statements.In the first statement, "if a figure is a rhombus" is p and "then the figure is a parallelogram" is q.In the second statement, "if a figure is a parallelogram" is q and "then the figure has two pairs of opposite sides that are parallel" is r.
STEP 3
Apply the Law ofyllogism.According to the Law ofyllogism, if "if p then q" and "if q then r" are true, then "if p then r" is also true.So, we can combine the two statements to form a new conditional statement "If a figure is a rhombus, then the figure has two pairs of opposite sides that are parallel."
The new conditional statement is "If a figure is a rhombus, then the figure has two pairs of opposite sides that are parallel."
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