Question

identifying subsets
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:

Step1: Recall the definition of a subset

A set \( A \) is a subset of a set \( B \) (denoted \( A \subseteq B \)) if every element of \( A \) is also an element of \( B \).

Step2: Analyze each set

• For set \( C \): A circle is not a parallelogram (a parallelogram is a quadrilateral with two pairs of parallel sides; a circle is a curved figure). So \( C

ot\subseteq P \).

• For set \( K \): A kite is a quadrilateral with two distinct pairs of adjacent sides equal. A general kite does not have two pairs of parallel sides (only some special kites, like rhombuses, are parallelograms, but not all kites). So \( K

ot\subseteq P \) (in general).

• For set \( R \): A rectangle is a quadrilateral with four right angles. By definition, a rectangle has two pairs of parallel sides (opposite sides are parallel and equal). So every rectangle is a parallelogram. Thus, \( R \subseteq P \).
• For set \( T \): A trapezoid (in the general definition) has at least one pair of parallel sides. A parallelogram has two pairs of parallel sides. Not all trapezoids are parallelograms (e.g., a trapezoid with only one pair of parallel sides is not a parallelogram). So \( T

ot\subseteq P \) (in general, depending on the definition; but the standard definition for subset here would exclude it as not all trapezoids are parallelograms).

Answer:

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