Question

for the given set first calculate the number of subsets for the set then calculate the number of proper subsets. {19, 17, 0, 5}

Answer 1

Step 1: Write out the formula

Given a set A, then the number of subsets the set A can have is given by

`\begin{gathered} \text{ number of subsets of A = }2^(|A|) \\ \text{and } \\ \text{ number of proper subsets of A = }2^(|A|)-1 \\ \text{ where} \\ |A|\text{ = the cardinality of A, that is the number of distinct elements of A} \end{gathered}`

Step 2: Write out the given values and substitute them into the formula

`\begin{gathered} A=\mleft\lbrace19,17,0,5\mright\rbrace \\ \text{therefore} \\ |A|=4 \\ \text{Hence,} \\ \text{ number of subsets of A = }2^4=16 \end{gathered}`
`\begin{gathered} \text{and } \\ \text{ number of proper subsets of A = }2^4-1=16-1=15 \end{gathered}`

Therefore, the number of possible subsets and proper subsets of the set {19,17,0,5} are 16 and 15 respectively