Question -
Answer -
A = {x : x एक प्राकृत संख्या है} = {1, 2, 3, 4……} B = {x : x एक समं प्राकृत संख्या है} = {2, 4, 6, 8…} C = {x : x एक विषम प्राकृत संख्या है} = {1, 3, 5, 7…} D = {x : x एक अभाज्य संख्या है} = {2, 3, 5, 7, 11….}
(i) A ∩ B = {1, 2, 3, 4….} ∩{2, 4, 6, 8….} = {2, 4, 6, 8….} = B
(ii) A ∩C = {1, 2, 3, 4……} ∩ {1, 3, 5, 7….} = {1, 3, 5, 7….} = C
(iii) A ∩D = {1, 2, 3, 4…} ∩ {2, 3, 5, 7…..} = {2, 3, 5, 7……} = D
(iv) B ∩ C = {2, 4, 6, 8…} ∩ {1, 3, 5, 7……} = Φ
(v) B ∩D = {2, 4, 6, 8…..} ∩ {2, 3, 5, 7…..} = {2}
(vi) C ∩D = {1, 3, 5, 7…..} ∩{2, 3, 5, 7, 11…….} = {3, 5, 7, 11, 13……} = {x : x एक विषम अभाज्य संख्या}