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Mathematics and Statistics · Class 11 Commerce

Ch 1Sets and Relations — Class 11 Mathematics and Statistics, concept-first.

Much of the mathematics used in commerce and statistics — grouping customers by region, classifying products, describing the set of possible outcomes of a business decision — begins with the simple idea of a collection. A set is a well-defined collection of distinct objects.

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Key concepts

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Sets and Their Representation

A set is a well-defined collection of distinct objects; its members are its elements, with meaning belongs to and meaning it does not. Because elements are distinct and unordered, is just and .

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

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Sets and Their Representation

Much of the mathematics used in commerce and statistics — grouping customers by region, classifying products, describing the set of possible outcomes of a business decision — begins with the simple id…

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Types of Sets

Once sets can be described, it is useful to classify them and to describe how one set can sit inside another.

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Operations on Sets

Sets can be combined to form new sets. These operations are best pictured with a Venn diagram, in which the universal set is drawn as a rectangle and the sets inside it as circles; overlapping circles…

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Ordered Pairs and Cartesian Product

So far the order of elements inside a set did not matter. But many real situations pair two things in a definite order — a product with its price, a year with its sales figure, an -coordinate with a -…

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Relations

A relation captures the idea that some pairs of objects are connected by a rule while others are not — "is the price of", "is older than", "is the capital of".

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Types of Relations

Relations defined on a single set (subsets of ) can have special structural properties. Three properties are especially important.

Exercises

+Show 7 questions7 questions
  1. Q10Write the set $B = \{x : x \in \mathbb{Z},\ -3 \le x < 2\}$ in roster form and state $n(B)$.Free
  2. Q11A set $A$ has $16$ subsets in total. How many elements does $A$ have, and how many proper subsets does it have?Free
  3. Q12For $U = \{1, 2, 3, \dots, 9\}$, $A = \{2, 4, 6, 8\}$ and $B = \{1, 2, 3, 4\}$, find (i) $A \cap B$, (ii) $A \cup B$, (iii) $B - A$, (iv) $(…Free
  4. Q13In a class of $40$ students, $30$ passed in Accountancy and $25$ passed in Economics; $20$ passed in both subjects. How many students passed…Preview
  5. Q14If $A = \{x, y\}$ and $B = \{1, 2, 3\}$, write $A \times B$ and state $n(A \times B)$.Preview
  6. Q15Let $A = \{1, 2, 3, 4, 5\}$. A relation $R$ on $A$ is defined by $R = \{(a, b) : b = a + 1\}$. Write $R$ in roster form and state its domain…Preview
  7. Q16On the set $A = \{1, 2, 3\}$, examine whether $R = \{(1, 1), (2, 2), (1, 2)\}$ is reflexive, symmetric and transitive.Preview

More questions

+Show 9 questions9 questions
  1. Example 1Write the set $A = \{x : x \in \mathbb{N},\ x \text{ is a divisor of } 12\}$ in roster form, and write the set $\{2, 4, 6, 8, 10\}$ in set-b…Free
  2. Example 2If $A = \{a, b, c\}$, write down the power set $P(A)$ and state $n(P(A))$ and the number of proper subsets of $A$.Free
  3. Example 3Let $U = \{1, 2, 3, \dots, 10\}$, $A = \{1, 2, 3, 4, 5\}$ and $B = \{4, 5, 6, 7\}$. Find (i) $A \cup B$, (ii) $A \cap B$, (iii) $A - B$, (iv…Free
  4. Example 4In a survey of $100$ investors, $60$ hold shares and $45$ hold mutual funds; $25$ hold both. How many hold (i) shares or mutual funds (at le…Preview
  5. Example 5For $U = \{1,2,3,4,5,6,7,8\}$, $A = \{1,2,3,4\}$ and $B = \{3,4,5,6\}$, verify De Morgan's law $(A \cup B)' = A' \cap B'$.Preview
  6. Example 6If $A = \{1, 2\}$ and $B = \{3, 4, 5\}$, find $A \times B$, $B \times A$, and $n(A \times B)$. Is $A \times B = B \times A$?Preview
  7. Example 7If $A \times B = \{(1, p),\ (1, q),\ (2, p),\ (2, q)\}$, find the sets $A$ and $B$.Preview
  8. Example 8Let $A = \{1, 2, 3, 4\}$ and $B = \{1, 4, 9, 16\}$. A relation $R$ from $A$ to $B$ is defined by $R = \{(a, b) : b = a^{2},\ a \in A,\ b \in…Preview
  9. Example 9On the set $A = \{1, 2, 3\}$, a relation is given by $R = \{(1,1),(2,2),(3,3),(1,2),(2,1)\}$. Determine whether $R$ is reflexive, symmetric…Preview