Question

A={a, b, p}, B={2, 3}, C={p, q, r, s} then n[(AUC) ×B] is

Answer 1

Answer:

n[(AUC) x B] = {(a,2)(a,3)(b,2)(b,3)(p,2)(p,3)(q,2)(q,3)(r,2)(r,3)(s,2)(s,3)}

Step-by-step explanation:

(AUC) = {a,b,p,q,r,s}

n[(AUC) x B] = {a,b,p,q,r,s} x {2,3}

= {(a,2)(a,3)(b,2)(b,3)(p,2)(p,3)(q,2)(q,3)(r,2)(r,3)(s,2)(s,3)}

Answer 2

Step-by-step explanation:

Given :-

A={a, b, p},

B={2, 3},

C={p, q, r, s}

To find :-

Find n[(AUC) ×B] ?

Solution :-

Method-1:-

Given sets are :

A = {a, b, p},

B = {2, 3},

C = {p, q, r, s}

AUC = { a,b,p } U { p,q,r,s }

=> AUC = { a,b,p,q,r,s }

Now

(AUC) × B

=> { a,b,p,q,r,s } × { 2,3 }

=> { ( a,2),(a,3),(b,2),(b,3),(p,2),(p,3),(q,2),(q,3),(r,2),

(r,3),(s,2),(s,3) }

The number of elements in (AUC) × B = 12

Method-2:-

Given sets are :

A = {a, b, p},

B = {2, 3},

C = {p, q, r, s}

AUC = { a,b,p } U { p,q,r,s }

=> AUC = { a,b,p,q,r,s }

We know that

If the number of elements in A is m and the number of elements in B is n then n(A×B) is m×n

n(AUC) = 6

n(B) = 2

=> n[(AUC)×B] = 6×2 = 12

Answer:-

n[(AUC) × B ] for the given problem is 12

Used formulae :-

If A and B are two non-empty sets then ,

→ The set of all elements in either in A or in B or in both is called the Union of the sets A and B and it is denoted by AUB .

→ AUB = { X:X€ A or X€B }

→ The set of all ordered pairs in which the first element belongs to A and the second element belongs to B is called The Cartesian Product of A and B and it is denoted by A×B .

→ The number of elements in a set A is called the Cardinal number of A and it is denoted by n(A).

→ If n(A) = m and n(B) = n then n(A×B) = m×n

→€ represents "belongs to ".