Use the given diagram to find - i-A-B- C- ii-B-A-C- iii-A-B- iv-A- B- Is-A- B-A-B-

(i) B∩ C={d,e,f,g,h,j}∩{h,i,j,k,l} ={h,j} ∴ A∪ (B∩ C)={a,b,c,d,g,h,i}∪{h,j} ={a,b,c,d,g,h,i,j} Ans. (ii) A C={a,b,c,d,g,h,i} {h,i,j,k,l} ={a,b,c,d, ...

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Byju's Answer

Standard VIII

Mathematics

Difference of Two Sets

Use the given...

Question

Use the given diagram to find :

$(i) A \cup (B \cap C) (i i) B - (A - C) (i i i) A - B (i v) A \cap B^{'} I s A \cup B^{'} = A - B ?$

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Solution

$(i) B \cap C = {d, e, f, g, h, j} \cap {h, i, j, k, l} = {h, j} ∴ A \cup (B \cap C) = {a, b, c, d, g, h, i} \cup {h, j} = {a, b, c, d, g, h, i, j} A n s . (i i) A - C = {a, b, c, d, g, h, i} - {h, i, j, k, l} = {a, b, c, d, g} ∴ B - (A - C) = {d, e, f, g, h, j} - {a, b, c, d, g} = {e, g, h, j} A n s . (i i i) A - B = {a, b, c, d, g, h, i} - {d, e, f, g, h, i} \Rightarrow A - B = {a, b, c, i} A n s . (i v) B^{'} = {a, b, c, i, k, l, m, n, p} A \cap B^{'} = {a, b, c, d, g, h, i} \cap {a, b, c, i, k, l, m, n, p} \Rightarrow A \cap B^{'} = {a, b, c, i} . . . . (I I)$

From I and II we can conclude $A \cap B^{'} = A - B$

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

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a \subset \{a, b, c\}

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\{a\} \in \{a, b, c\}

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Use the given diagram to find : (i) A∪(B∩C)(ii) B−(A−C)(iii) A−B(iv) A∩B′Is A∪B′=A−B?

Use the given diagram to find :

$(i) A \cup (B \cap C) (i i) B - (A - C) (i i i) A - B (i v) A \cap B^{'} I s A \cup B^{'} = A - B ?$