Mathematics - Functions Question with Solution | TestHub

Hint: Let $Y_i$ be the subset of $X$ such that $y_i=7m+i,m\in I$ $Y_0=\{7,14,\dots ..98\},n\left(Y_0\right)=14$ ${\mathrm{Y}}_1=\{1,8,15\dots 99\},\mathrm{n}\left({\mathrm{Y}}_1\right)=15$ $Y_2=\{2,9,16\dots ,100\},n\left(Y_2\right)=15$ $Y_3=\{3,10,16\dots .94\},n{Y}_3)=14$ $Y_4=\{4,11,18\dots 95\},n\left(Y_4\right)=14$ $Y_5=\{5,12,\dots .96\},n{Y}_5)=14$ $Y_6=\{6,13,\dots .97\},n\left(Y_6\right)=14$

The largest $Y$ will consist of (!) an element of $Y_0$ (ii) $Y_1$ (iii) $Y_2$ (iv) $Y_3$ or $Y_4$

⇒ The maximum possible number of elements in $Y=1+15+15+14=45$.