From the given diagram find - i-A- B- ii-A- B- iii-A-B- iv-B-A- v-A- B-

(i) A∪ B={a,c,d,e}∪{b,c,e,f} ⇒ A∪ B={a,b,c,d,e,f} (ii) A'={b,f,g,h} A'∩ B={b,f,g,h}]∩{b,c,e,f} ⇒ A'∩ B={b,f} (iii) A B={a,c,d,e} {b,c,e,f} ⇒ A B={a,d} (iv) ...

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Standard VIII

Mathematics

Difference of Two Sets

From the give...

Question

From the given diagram find :

$(i) A \cup B (i i) A^{'} \cap B (i i i) A - B (i v) B - A (v) (A \cup B)^{'}$

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Solution

$(i) A \cup B = {a, c, d, e} \cup {b, c, e, f} \Rightarrow A \cup B = {a, b, c, d, e, f} (i i) A^{'} = {b, f, g, h} A^{'} \cap B = {b, f, g, h}] \cap {b, c, e, f} \Rightarrow A^{'} \cap B = {b, f} (i i i) A - B = {a, c, d, e} - {b, c, e, f} \Rightarrow A - B = {a, d} (i v) B - A = {b, c, e, f} - {a, c, d, e} = {b, f} (v) A \cup B = {a, b, c, d, e, f} ∴ (A \cup B)^{'} = {h, g}$

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From the given diagram find : (i) A∪B(ii) A′∩B(iii) A−B(iv) B−A(v) (A∪B)′

(i) A∪B={a,c,d,e}∪{b,c,e,f}⇒ A∪B={a,b,c,d,e,f}(ii) A′={b,f,g,h}A′∩B={b,f,g,h}]∩{b,c,e,f}⇒ A′∩B={b,f}(iii) A−B={a,c,d,e}−{b,c,e,f}⇒ A−B={a,d}(iv) B−A={b,c,e,f}−{a,c,d,e} ={b,f}(v) A∪B={a,b,c,d,e,f}∴ (A∪B)′={h,g}

From the given diagram find :

$(i) A \cup B (i i) A^{'} \cap B (i i i) A - B (i v) B - A (v) (A \cup B)^{'}$