Set basic conceptual question, please help, I need descriptive answer.

[naajhat]

Let A={5,6,7} ; B = {8,9,10} C = {1,2,3,4,5,6,7,8,9,10} then find
(i) number of subsets of C which are supersets of B.
(ii) number of subsets of C having number of element of A and B.
(iii) number of subsets of C having exactly one element from each of A and B.

 

[Deleted member 4993]

Let A={5,6,7} ; B = {8,9,10} C = {1,2,3,4,5,6,7,8,9,10} then find
(i) number of subsets of C which are supersets of B.
(ii) number of subsets of C having number of element of A and B.
(iii) number of subsets of C having exactly one element from each of A and B.

According to your textbook/Google - what are the definition s of:

Sub-set and

Super-set.

 

[naajhat]

According to your textbook/Google - what are the definition s of:

Sub-set and

Super-set.

A set A is a subset of set B when the elements of set A are present in set B. In the same context set B is a superset of set A.

 

[Deleted member 4993]

A set A is a subset of set B when the elements of set A are present in set B. In the same context set B is a superset of set A.

Great! Now apply those definition s to your assignment.

 

[naajhat]

Great! Now apply those definition s to your assignment.

According to book

If X is a superset B and subset of C, then X has at least 3 elements i.e, 8,9 and 10

Now each of the reaming elements of C except for 8,9,19 i.e, 1,2,3,4,5,6,7 has two choices either they would belong to X or does not belong to X.
Thus total number of X's = 2*2*2*2*2*2*2 = 123

My approach is in the attached file.

I couldn't understand the approach of the book . I kinda found a way to calculate the answer but I'm not conceptually clear. Can you please describe it conceptually.

 

[naajhat]

According to book

If X is a superset B and subset of C, then X has at least 3 elements i.e, 8,9 and 10

Now each of the reaming elements of C except for 8,9,19 i.e, 1,2,3,4,5,6,7 has two choices either they would belong to X or does not belong to X.
Thus total number of X's = 2*2*2*2*2*2*2 = 128

My approach is in the attached file.

I couldn't understand the approach of the book . I kinda found a way to calculate the answer but I'm not conceptually clear. Can you please describe it conceptually.

sorry, 2^7 is 128

 

[pka]

sorry, 2^7 is 128

Any finite set that has [imath]N[/imath] elements has [imath]2^N[/imath] subsets.
If [imath]X[/imath] is any subset of [imath]\{1,2,3,4,5,6,7\}[/imath] (there are [imath]2^7[/imath]) then [imath]X\cup\{8,9,10\}[/imath] is a super set of [imath]\{8,9,10\}[/imath].