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Q2(ii):
Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (ii) 8 . . . A
Solution :
Step 1: Analyzing the Set Definition
The set $A$ is defined by the roster method as $A = \{1, 2, 3, 4, 5, 6\}$. This implies that the set contains exactly six distinct elements: $1, 2, 3, 4, 5, \text{and } 6$. Any value not present within these curly braces is strictly excluded from the set [Per the definition of set membership].
Step 2: Verification of Element Inclusion
We test the candidate element $x = 8$ against the set $A$:
- The set $A$ contains integers $n$ such that $1 \le n \le 6$ and $n \in \mathbb{Z}^+$.
- Comparing $8$ to the elements of $A$:
- $8 \neq 1, 8 \neq 2, 8 \neq 3, 8 \neq 4, 8 \neq 5, 8 \neq 6$.
Step 3: Logical Application of Symbols
The symbol $\in$ denotes "is an element of," implying a truth value of $True$ if the element is contained within the set. The symbol $\notin$ denotes "is not an element of," implying a truth value of $True$ if the element is not found within the set [By Axiom of Extensionality].
Step 4: Conclusion
Since the number $8$ is not included in the listing of elements for set $A$, the correct relation is expressed as $8 \notin A$.
Final Solution: 8 $\notin$ A
More Questions from Class 11 Mathematics Sets EXERCISE 1.1
- Q1(i): Which of the following are sets ? Justify your answer. (i) The collection of all the months of a year beginning with the letter J.
- Q1(ii): Which of the following are sets ? Justify your answer. (ii) The collection of ten most talented writers of India.
- Q1(iii): Which of the following are sets ? Justify your answer. (iii) A team of eleven best-cricket batsmen of the world.
- Q1(iv): Which of the following are sets ? Justify your answer. (iv) The collection of all boys in your class.
- Q1(ix): Which of the following are sets ? Justify your answer. (ix) A collection of most dangerous animals of the world.
- Q1(v): Which of the following are sets ? Justify your answer. (v) The collection of all natural numbers less than 100.
- Q1(vi): Which of the following are sets ? Justify your answer. (vi) A collection of novels written by the writer Munshi Prem Chand.
- Q1(vii): Which of the following are sets ? Justify your answer. (vii) The collection of all even integers.
- Q1(viii): Which of the following are sets ? Justify your answer. (viii) The collection of questions in this Chapter.
- Q2(i): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (i) 5. . .A
- Q2(iii): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (iii) 0. . .A
- Q2(iv): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (iv) 4. . . A
- Q2(v): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (v) 2. . .A
- Q2(vi): Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces: (vi) 10. . .A
- Q3(i): Write the following sets in roster form: (i) $A = \{x : x$ is an integer and $–3 \le x < 7\}$
- Q3(ii): Write the following sets in roster form: (ii) $B = \{x : x$ is a natural number less than 6\}
- Q3(iii): Write the following sets in roster form: (iii) $C = \{x : x$ is a two-digit natural number such that the sum of its digits is 8\}
- Q3(iv): Write the following sets in roster form: (iv) $D = \{x : x$ is a prime number which is divisor of 60\}
- Q3(v): Write the following sets in roster form: (v) $E$ = The set of all letters in the word TRIGONOMETRY
- Q3(vi): Write the following sets in roster form: (vi) $F$ = The set of all letters in the word BETTER
- Q4(i): Write the following sets in the set-builder form : (i) $\{3, 6, 9, 12\}$
- Q4(ii): Write the following sets in the set-builder form : (ii) $\{2,4,8,16,32\}$
- Q4(iii): Write the following sets in the set-builder form : (iii) $\{5, 25, 125, 625\}$
- Q4(iv): Write the following sets in the set-builder form : (iv) $\{2, 4, 6, . . .\}$
- Q4(v): Write the following sets in the set-builder form : (v) $\{1,4,9, . . .,100\}$
- Q5(i): List all the elements of the following sets : (i) $A = \{x : x$ is an odd natural number\}
- Q5(ii): List all the elements of the following sets : (ii) $B = \{x : x$ is an integer, $– \frac{1}{2} < x < \frac{9}{2}\}$
- Q5(iii): List all the elements of the following sets : (iii) $C = \{x : x$ is an integer, $x^2 \le 4\}$
- Q5(iv): List all the elements of the following sets : (iv) $D = \{x : x$ is a letter in the word “LOYAL”\}
- Q5(v): List all the elements of the following sets : (v) $E = \{x : x$ is a month of a year not having 31 days\}
- Q5(vi): List all the elements of the following sets : (vi) $F = \{x : x$ is a consonant in the English alphabet which precedes $k$ \}.
- Q6: Match each of the set on the left in the roster form with the same set on the right described in set-builder form: (i) $\{1, 2, 3, 6\}$ (a) $\{x : x$ is a prime number and a divisor of 6\} (ii) $\{2, 3\}$ (b) $\{x : x$ is an odd natural number less than 10\} (iii) $\{M,A,T,H,E,I,C,S\}$ (c) $\{x : x$ is natural number and divisor of 6\} (iv) $\{1, 3, 5, 7, 9\}$ (d) $\{x : x$ is a letter of the word MATHEMATICS\}.
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