Question

consider the following sets: p = {x | x is a parallelogram} c = {x | x is a circle} k = {x | x is a kite} r = {x | x is a rectangle} t = {x | x is a trapezoid} which set is a subset of set p? c k r t

Explanation:

To determine which set is a subset of \( P = \{x \mid x \text{ is a parallelogram}\} \), we recall the definition of a parallelogram: a quadrilateral with both pairs of opposite sides parallel.

• A circle (set \( C \)) is not a quadrilateral, so \( C \) is not a subset of \( P \).
• A kite (set \( K \)) has two pairs of adjacent sides equal but not necessarily both pairs of opposite sides parallel (in general), so most kites are not parallelograms.
• A rectangle (set \( R \)) is a quadrilateral with both pairs of opposite sides parallel (and four right angles), so all rectangles are parallelograms. Thus, \( R \subseteq P \).
• A trapezoid (set \( T \)) has only one pair of parallel sides (in the traditional definition) or at least one pair (in some definitions), but not necessarily both pairs, so not all trapezoids are parallelograms.

Answer:

R. \( R = \{x \mid x \text{ is a rectangle}\} \)