Note: This is the Solution of review exercise 3.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 3.1
Question 1: Write the following sets in set builder notation:
\((i)\) \(\quad\) \(\{1,4,9,16,25,36,\ldots, 484\} \)
\((ii)\) \(\quad\) \(\{2,4,8,16,32,64,\ldots,150\} \)
\((iii)\) \(\quad\) \(\{0, \pm 1, \pm 2, \ldots, \pm 1000\}\)
\((iv)\) \(\quad\) \(\{6,12,18,\ldots,120\} \)
\((v)\) \(\quad\)\( \{100,102,104,\ldots,400\}\)
\((vi)\) \( \quad\) \(\{1,3,9,27,81,\ldots\} \)
\((vii)\) \( \quad\) \(\{1,2,4,5,10,25,50,100\} \)
\((viii)\) \( \quad\) \(\{5,10,15,\ldots,100\} \)
\((ix)\) \( \quad\) The set of all integers between\(-100\) and \(1000 \)
Question 2: Write each of the following sets in tabular forms:
\((i)\) \(\quad\) \(\left\{x\mid x\text{ is a multiple of } 3\land x\le 35\right\} \)
\((ii)\) \(\quad\) \(\{x\mid x\in R\land 2x+1=0\} \)
\((iii)\) \(\quad\) \(\{{x\mid x\in P\land x< 12}\}\)
\((iv)\) \(\quad\) \( \left\{x\mid x\text{ is a divisor of } 128\right\}\)
\((v)\) \(\quad\)\(\left\{x \mid x=2^{n} ,n\in N\land n< 8\right\} \)
\((vi)\) \( \quad\) \(\{x \mid x\in N\land x+4=0\} \)
\((vii)\) \( \quad\) \(\{x \mid x\in N\land x=x\} \)
\((viii)\) \( \quad\) \( \{x \mid x\in Z\land 3x+1=0\} \)
Question 3: Write two proper subsets of each of the following sets:
\((i)\) \(\quad\) \( \{a,b,c\}\)
\((ii)\) \(\quad\) \(\{0,1\}\)
\((iii)\) \(\quad\) \(N \)
\((iv)\) \(\quad \)\(Z \)
\((v)\) \(\quad \) \(Q \)
\((vi)\) \(\quad \) \(R \)
\((vii)\) \(\quad \) \(\{x|x\in Q\land 0< x\leq 2\} \)
Question 4: Is there any set which has no proper subset? If so, name that set.
Question 5: What is the difference between \(\small{\{a,b\}}\) and \(\small{\{\{a,b\}\}}\)?
Question 6: What is the number of elements of the power set of each of the following sets?
\((i)\) \(\quad\) \(\{\ \}\)
\((ii)\) \(\quad\) \(\{0,1\}\)
\((iii)\) \(\quad\) \(\{1,2,3,4,5,6,7\}\)
\((iv)\) \(\quad \)\(\{0,1,2,3,4,5,6,7\}\)
\((v)\) \(\quad \)\(\{a,\{b,c\}\}\)
\((vi)\) \(\quad \)\(\{\{a,b\},\{b,c\},\{d,e\}\}\)
Question 7: Write down the power set of each of the following sets:
\((i)\) \(\quad\) \(\{\ 9,11\}\)
\((ii)\) \(\quad\) \(\{+,-, \times, \div\}\)
\((iii)\) \(\quad\) \(\{\phi\}\)
\((iv)\) \(\quad \)\(\{a,\{b,c\}\}\)