Question:

Let P be a set of squares, Q be set of parallelograms, R be a set of quadrilaterals and S be a set of rectangles. Consider the following : 1. P $\subset$ Q 2. R $\subset$ P 3. P $\subset$ S 4. S $\subset$ R Which of the above are correct?

Updated On: Jul 6, 2022
  • 1, 2 and 3
  • 1, 3 and 4
  • 1, 2 and 4
  • 3 and 4
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The Correct Option is B

Solution and Explanation

As given, P $\equiv$ set of square, Q $\equiv$ set of parallelogram, R $\equiv$ set of quadrilaterals and S $\equiv$ set of rectangles. Since all squares are parallelogram $\Rightarrow $ P $ \subset$ Q similarly. Since, all squares are rectangles P $ \subset$ S and are quadrilaterals $\Rightarrow $ S $ \subset$ R $\Rightarrow $ 1, 3 and 4 are correct
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Concepts Used:

Sets

Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.

Example of set: Set of vowels A={a,e,i,o,u}

Representation of Sets

There are three basic notation or representation of sets are as follows:

Statement Form: The statement representation describes a statement to show what are the elements of a set.

  • For example, Set A is the list of the first five odd numbers.

Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.

  • For example represent the set of vowels in roster form.

A={a,e,i,o,u}

Set Builder Form: 

  1. The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
  2. The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
  3. For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
  4. Sometimes a ":" is used in the place of the "|".