Question

P n (Q u R)U= {a,b,c,d.........x,y,zP= {T,O,D,A,Y}Q={L,O,N,G,I,T,U,D,E}R= {L,A,C,Q,U,E,R}

Answer 1

∪ = Union

∩ = Intersection

Let's find (Q u R):

$\begin{gathered} Q=\mleft\lbrace L,O,N,G,I,T,U,D,E\mright\rbrace \\ R=\mleft\lbrace L,A,C,Q,U,E,R\mright\rbrace \\ so\colon \\ Q\cup R=\mleft\lbrace L,O,N,G,I,T,U,D,E,L,A,C,Q,U,E,R\mright\rbrace \end{gathered}$

Now, we can find P n (Q u R):

$\begin{gathered} P=\mleft\lbrace T,O,D,A,Y\mright\rbrace \\ Q\cup R=\lbrace L,O,N,G,I,T,U,D,E,L,A,C,Q,U,E,R\rbrace \\ so\colon \\ P\cap(Q\cup R)=\mleft\lbrace T,O,D,A\mright\rbrace \end{gathered}$