Question

.12. If A = (1.2, 3, 4), B = {3.4.5.6) and C = 11.2.4. 6, 7), then find i) An(BUC) ii) A-(BUC)​

Answer 1

Answer:

Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's metabolic activities.

Answer 2

Step-by-step explanation:

A={1,2,3,4}

B={3,4,5,6}

C={4,5,6,7,8}

Universal set,X={1,2,3,4,5,6,7,8,9,10}

Verify

\sf A\cap (B\cup C)=(A\cap B)\cup(A\cap C)A∩(B∪C)=(A∩B)∪(A∩C)

Given:

A={1,2,3,4}

B={3,4,5,6}

C={4,5,6,7,8}

Universal set,X={1,2,3,4,5,6,7,8,9,10}

To Verify:

\sf A\cap (B\cup C)=(A\cap B)\cup(A\cap C)A∩(B∪C)=(A∩B)∪(A∩C)

Explanation:

Consider

\sf B\cup C =(3,4,5,6)\cup (4,5,6,7,8)B∪C=(3,4,5,6)∪(4,5,6,7,8)

\sf B\cup C=(3,4,5,6,7,8)B∪C=(3,4,5,6,7,8)

Consider

\sf LHS=A\cap (B\cup C)=(1,2,3,4)\cap (3,4,5,6,7,8)LHS=A∩(B∪C)=(1,2,3,4)∩(3,4,5,6,7,8)

LHS={3,4}--------(1)

Consider

\sf A\cap B=(1,2,3,4)\cap (3,4,5,6)=(3,4)A∩B=(1,2,3,4)∩(3,4,5,6)=(3,4)

\sf A\cap C=(1,2,3,4)\cup (4,5,6,7,8)=(4)A∩C=(1,2,3,4)∪(4,5,6,7,8)=(4)

\sf RHS=(A\cap B)\cup (A\cap C)RHS=(A∩B)∪(A∩C)

\sf RHS=(3,4)\cup (4)RHS=(3,4)∪(4)

RHS={3,4}---------(2)

From equation 1 and equation 2

LHS=RHS

Hence proved