Question

Write the cardinal number for the set $A=\left\{x:xisaletterinthewordIMPORTANT\right\}$.

Answer 1

Cardinal number is the number of elements in a set.

The elements for set $A$ will be letters in the word $\mathbf{IMPORTANT}$.

Therefore the letters will be $\mathbf{I}\mathbf{,}\mathbf{}\mathbf{M}\mathbf{,}\mathbf{}\mathbf{P}\mathbf{,}\mathbf{}\mathbf{O}\mathbf{,}\mathbf{}\mathbf{R}\mathbf{,}\mathbf{}\mathbf{T}\mathbf{,}\mathbf{}\mathbf{A}\mathbf{,}\mathbf{}\mathbf{N}$. We do not repeat an element in a set, so $\mathbf{T}$ will be written only once.

Set in roster form will be $A=\left\{I,M,P,O,R,T,A,N\right\}$.

Hence, its cardinal number will be $n\left(A\right)=8$.