Questions

• 2

At 23:00 , we say that f(EUF) = f(E) U f(F)

Sir, when you give the example Wives(Indians U Software Engineer) = Wives(Indians) U Wives(Software Engineer) , dont we need to subtract the components where Wives(Indian Software engineer) as this will be repeated

Also given that E and F are both subsets of A, there is bound to be common elements between them.

Or do we ignore the duplicate items because it is a set, and duplicate items are not included in set.

• getgatebook

when A = {1,2,3} and B = {1,5,6} A U B = {1,2,3,5,6}. Here union operation automatically eliminates duplicates as that is the way set union is defined.

• 1

@18:43

sabi7habi7

sir, you have given a counter example with an element 7. wat if 7 has a
different image in C than all the elements in B

• getgatebook

If 7 is mapped to new element 11 then h is not on to right ? But in the question it is given that h is on to.
One more point, some how if you find an arrangement such that h is on to and f and g both are on to then we can not say option D is correct. Think why ?

• 1

At 10:00 2nd gate problem

sudiptasenpro

all n subsets X1, X2, … Xn are of size 3.
So total number of elements in Xj in 3n.
So ans = 3n
is it correct? Summing up the no of elements in all Xj gives nothing but the count of repetitions of all the elements of S

• getgatebook

Yes, you are absolutely correct.

• 2

@19:06

sagarsharmapro21

Hi Sir,
f : A -> B
E and F are subsets of A
Considering following example
A(Domain) = {1,2,3}
B(images) = All subsets of A{{}{1}{2}{3}{1,2}{2,3}{1,3}{1,2,3}}
As mentioned in the question E and F being subsets of A(Domain) – E {{1},{1,3},{2,3}} and F = {{2},{2,3}}

If I take the below example instead of Indian and software engineer and if
function is f(i) = i
Then
f(E U F) = f({{1},{1,3},{2,3}} U {{2},{2,3}}) = {{1},{1,3}{2}{2,3}}

f(E ∩ F) = f({{1},{1,3},{2,3}} ∩ {{2},{2,3}}) = f({2,3})
f({2,3}) = {2,3} This is same as following :

f(E) = f({{1},{1,3},{2,3}}) = {{1},{1,3},{2,3}}
f(F) = f({{2},{2,3}}) = {{2},{2,3}}
f(E) ∩ f(F) = {2,3}.