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Q4(iii):
If $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, $C = \{5, 6, 7, 8 \}$and $D = \{ 7, 8, 9, 10 \}$; find (iii) $B \cup C$
Solution :
Given Sets
The sets provided for the calculation are defined as follows:
- $A = \{1, 2, 3, 4\}$
- $B = \{3, 4, 5, 6\}$
- $C = \{5, 6, 7, 8\}$
- $D = \{7, 8, 9, 10\}$
Step 1: Theoretical Definition of Union
The union of two sets, denoted as $B \cup C$, is the set of all elements which are members of either set $B$, set $C$, or both [Per the definition of Set Union in Zermelo-Fraenkel set theory].
Formally: $B \cup C = \{x : x \in B \text{ or } x \in C\}$.
Step 2: Listing Elements of B and C
Identify all distinct elements present in either set:
- Elements of $B$: $3, 4, 5, 6$
- Elements of $C$: $5, 6, 7, 8$
Step 3: Combining and Removing Duplicates
Per the Fundamental Principle of Set Representation, every element must be unique within a set [Principle of Extensionality]. We aggregate the elements and ensure no value is repeated:
$B \cup C = \{3, 4, 5, 6\} \cup \{5, 6, 7, 8\}$
$B \cup C = \{3, 4, 5, 6, 5, 6, 7, 8\}$
Removing duplicate values ($5$ and $6$):
$B \cup C = \{3, 4, 5, 6, 7, 8\}$
Visual Representation (Venn Diagram)
Final Solution: $B \cup C = \{3, 4, 5, 6, 7, 8\}$
More Questions from Class 11 Mathematics Sets EXERCISE 1.4
- Q1(i): Find the union of each of the following pairs of sets : (i) $X = \{1, 3, 5\} Y = \{1, 2, 3\}$
- Q1(ii): Find the union of each of the following pairs of sets : (ii) $A = \{ a, e, i, o, u\} B = \{a, b, c\}$
- Q1(iii): Find the union of each of the following pairs of sets : (iii) $A = \{x : x$ is a natural number and multiple of 3\} $B = \{x : x$ is a natural number less than 6\}
- Q1(iv): Find the union of each of the following pairs of sets : (iv) $A = \{x : x$ is a natural number and $1 < x \le 6$ \} $B = \{x : x$ is a natural number and $6 < x < 10$ \}
- Q1(v): Find the union of each of the following pairs of sets : (v) $A = \{1, 2, 3\}$, $B = \phi$
- Q2: Let $A = \{ a, b \}$, $B = \{a, b, c\}$. Is $A \subset B$ ? What is $A \cup B$ ?
- Q3: If $A$ and $B$ are two sets such that $A \subset B$, then what is $A \cup B$ ?
- Q4(i): If $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, $C = \{5, 6, 7, 8 \}$and $D = \{ 7, 8, 9, 10 \}$; find (i) $A \cup B$
- Q4(ii): If $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, $C = \{5, 6, 7, 8 \}$and $D = \{ 7, 8, 9, 10 \}$; find (ii) $A \cup C$
- Q4(iv): If $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, $C = \{5, 6, 7, 8 \}$and $D = \{ 7, 8, 9, 10 \}$; find (iv) $B \cup D$
- Q4(v): If $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, $C = \{5, 6, 7, 8 \}$and $D = \{ 7, 8, 9, 10 \}$; find (v) $A \cup B \cup C$
- Q4(vi): If $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, $C = \{5, 6, 7, 8 \}$and $D = \{ 7, 8, 9, 10 \}$; find (vi) $A \cup B \cup D$
- Q4(vii): If $A = \{1, 2, 3, 4\}$, $B = \{3, 4, 5, 6\}$, $C = \{5, 6, 7, 8 \}$and $D = \{ 7, 8, 9, 10 \}$; find (vii) $B \cup C \cup D$
- Q5: Find the intersection of each pair of sets of question 1 above.
- Q6(i): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (i) $A \cap B$
- Q6(ii): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (ii) $B \cap C$
- Q6(iii): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (iii) $A \cap C \cap D$
- Q6(iv): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (iv) $A \cap C$
- Q6(ix): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (ix) $( A \cap B ) \cap ( B \cup C )$
- Q6(v): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (v) $B \cap D$
- Q6(vi): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (vi) $A \cap (B \cup C)$
- Q6(vii): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (vii) $A \cap D$
- Q6(viii): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (viii) $A \cap (B \cup D)$
- Q6(x): If $A = \{ 3, 5, 7, 9, 11 \}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (x) $( A \cup D) \cap ( B \cup C)$
- Q7(i): If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (i) $A \cap B$
- Q7(ii): If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (ii) $A \cap C$
- Q7(iii): If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (iii) $A \cap D$
- Q7(iv): If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (iv) $B \cap C$
- Q7(v): If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (v) $B \cap D$
- Q7(vi): If $A = \{x : x$ is a natural number \}, $B = \{x : x$ is an even natural number\} $C = \{x : x$ is an odd natural number\} and $D = \{x : x$ is a prime number \}, find (vi) $C \cap D$
- Q8(i): Which of the following pairs of sets are disjoint (i) $\{1, 2, 3, 4\}$ and $\{x : x$ is a natural number and $4 \le x \le 6$ \}
- Q8(ii): Which of the following pairs of sets are disjoint (ii) $\{ a, e, i, o, u \}$ and $\{ c, d, e, f \}$
- Q8(iii): Which of the following pairs of sets are disjoint (iii) $\{x : x$ is an even integer \}$ and $\{x : x$ is an odd integer\}
- Q9(i): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (i) $A – B$
- Q9(ii): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (ii) $A – C$
- Q9(iii): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (iii) $A – D$
- Q9(iv): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (iv) $B – A$
- Q9(ix): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (ix) $C – B$
- Q9(v): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (v) $C – A$
- Q9(vi): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (vi) $D – A$
- Q9(vii): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (vii) $B – C$
- Q9(viii): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (viii) $B – D$
- Q9(x): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (x) $D – B$
- Q9(xi): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (xi) $C – D$
- Q9(xii): If $A = \{3, 6, 9, 12, 15, 18, 21\}$, $B = \{ 4, 8, 12, 16, 20 \}$, $C = \{ 2, 4, 6, 8, 10, 12, 14, 16 \}$, $D = \{5, 10, 15, 20 \}$; find (xii) $D – C$
- Q10(i): If $X= \{ a, b, c, d \}$ and $Y = \{ f, b, d, g\}$, find (i) $X – Y$
- Q10(ii): If $X= \{ a, b, c, d \}$ and $Y = \{ f, b, d, g\}$, find (ii) $Y – X$
- Q10(iii): If $X= \{ a, b, c, d \}$ and $Y = \{ f, b, d, g\}$, find (iii) $X \cap Y$
- Q11: If $R$ is the set of real numbers and $Q$ is the set of rational numbers, then what is $R – Q$?
- Q12(i): State whether each of the following statement is true or false. Justify your answer. (i) \{ 2, 3, 4, 5 \} and \{ 3, 6\} are disjoint sets.
- Q12(ii): State whether each of the following statement is true or false. Justify your answer. (ii) \{ a, e, i, o, u \} and \{ a, b, c, d \}are disjoint sets.
- Q12(iii): State whether each of the following statement is true or false. Justify your answer. (iii) \{ 2, 6, 10, 14 \} and \{ 3, 7, 11, 15\} are disjoint sets.
- Q12(iv): State whether each of the following statement is true or false. Justify your answer. (iv) \{ 2, 6, 10 \} and \{ 3, 7, 11\} are disjoint sets.
CBSE Solutions for Class 11 Mathematics Sets
Chapters in CBSE - Class 11 Mathematics
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