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Q10(i):
If $X= \{ a, b, c, d \}$ and $Y = \{ f, b, d, g\}$, find (i) $X – Y$
Solution :
Step 1: Theoretical Definition of Set Difference
The set difference of two sets $X$ and $Y$, denoted as $X - Y$ (or $X \setminus Y$), is defined as the set of all elements that are members of $X$ but are not members of $Y$. Mathematically, this is expressed as:
$X - Y = \{ x : x \in X \text{ and } x \notin Y \}$
[Per the Axiom of Specification in Zermelo-Fraenkel set theory]
Step 2: Identification of Given Elements
The sets provided are:
- $X = \{ a, b, c, d \}$
- $Y = \{ f, b, d, g \}$
Step 3: Comparative Analysis and Element Filtering
We evaluate each element $x \in X$ to determine if it exists in $Y$:
| Element ($x \in X$) | Status in $Y$ | Action |
|---|---|---|
| $a$ | $a \notin Y$ | Keep in result |
| $b$ | $b \in Y$ | Discard |
| $c$ | $c \notin Y$ | Keep in result |
| $d$ | $d \in Y$ | Discard |
Step 4: Vector-Set Visualization
Step 5: Final Set Construction
By retaining only those elements found in $X$ that are absent in $Y$, we collect the remaining elements $\{a, c\}$.
Final Solution: $X - Y = \{ a, c \}$
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(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) $B \cup C$
- 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(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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