doing s home work for a math class on logic an reasoning

If a shape is a parallelogram, then the shape has four sides.

If a shape has four sides, then it is a quadrilateral.

 

Therefore, if a shape is a parallelogram, then it is a quadrilateral.

 

A.  Is this a valid argument?

 

B.  Explain why or why not.
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1 Answer

A) It is a valid argument. A parallelogram is a special case of a quadrilateral.

B) This can be explained in terms of sets and subsets. The set of quadrilaterals is a subset of polygons. Trapezoids form a subset of quadrilaterals. The set of parallelograms is another subset of the set of quadrilaterals. The set of squares is a subset of the set of parallelograms, as is the subset of rhombuses.

We can say that all parallelograms are quadrilaterals; but not all quadrilaterals are parallelograms.

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