Question

Hello,

I need help with this problem.

Please show the solution and all the steps that lead to it.

Thank you very much.

or ts A and

Answer 1

here A n B ={(T,H),(T,H)} ( (as (t,H) and {H,T} are the common elements)

A U B ={(H,H),(H,T),(T,H),(T,T)} (all elements in A and B)

A^c U B^c = {(H,H),(T,T)} (as (H,H) is not in A and (T,T) is not in B)

A^c n B^c ={ $\phi$ ​} (as there is no common elements in A^c and B^c)

(A n B)^c ={ {(H,H),(T,T)} (as {(H,H),(T,T)} are elements which are not in (A n B))

(A u B)^c ={ $\phi$ ​} (cause all sample space is in Au B therefore not (A U B) will be empty set_

from above (A n B)^c =A^c U B^c

and (A u B)^c = A^c n B^c

hence Demorgan' Law are verified