Difference of Sets
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Friends, iss article mein hum seekhenge ki sets ke Difference ka kya matlab hota hai aur agar hame do(two) sets diye gaye ho to unka Difference kaise find kar sakte hain! So, friends...
Maan lijiye A aur B koi do(two) set hain. To A aur B ka Difference (in the same order) wo set hota hai jisme set A ke wo elements aate hain jo set B mein nahi aate hain. Hum set A aur set B ke Difference ko symbolically 'A - B' se show karte hain aur isko 'A minus B' padhte hain (read karte hain). Example ke liye, maan lijiye A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8} then
A - B = {1, 2, 3, 4, 5, 6} - {2, 4, 6, 8}
= {1, 3, 5}.
Isi tarah se B - A = {2, 4, 6, 8} - {1, 2, 3, 4, 5, 6}
= {8}.
[Note:
(i) Set A aur B, chaahe A aur B koi se bhi sets ho, ke Difference ko set-builder form mein aise define kiya jaata hai- A - B = {x:x ∈ A or x ∉ B}
(ii) A - B ko A\B se bhi denote kiya jaata hai].
Chaliye 'Difference of Sets' ko aur better tarike se samajhne ke liye kuch aur examples dekh lete hain.
Ex.1. A = {a, e, i, o, u} and B = {a, i, u}. Find A - B. And B - A also.
Solution: A = {a, e, i, o, u}
B = {a, i, u}
A - B = {a, e, i, o, u} - {a, i, u}
= {e, o}
B - A = {a, i, u} - {a, e, i, o, u}
= { }
= Φ
Ex.2. If A = {1}, B = {1, 2, 5} and C = {1, 2, 3, 6, 7} then find A - B, B - C and A - C.
Solution: A = {1}
B = {1, 2, 5}
C = {1, 2, 3, 6, 7}
A - B = {1} - {1, 2, 5}
= { }
= Φ
B - C = {1, 2, 5} - {1, 2, 3, 6, 7}
= {5}
C - A = {1, 2, 3, 6, 7} - {1}
= {2, 3, 6, 7}
Ex.3. If set P = {x:x is a natural number and 1 < x ≤ 6} and set Q = {x:x is a natural number and 6 < x < 10}. Find P - Q.
Solution: P = {x:x is a natural number and 1 < x ≤ 6}
= {1, 2, 3, 4, 5, 6}
Q = {x:x is a natural number and 6 < x < 10}
= {7, 8, 9}
P - Q = {1, 2, 3, 4, 5, 6} - {7, 8, 9}
= {1, 2, 3, 4, 5, 6}
= {x:x is a natural number and 1 ≤ x < 7}.
Venn Diagram for Difference of Sets
Kinhi do(two) sets, maan lijiye set A aur set B, ke liye A - B aur B - A ka Venn diagram kuch aisa hota hai-
For A - B:
(i) Agar set A aur set B mein kuch common element ho (i.e., A⋂B ≠ Φ):
(ii) Agar set A aur set B mein kuch common element naa ho (i.e., A⋂B = Φ):
For B - A:
(i) Agar set A aur set B mein kuch common element ho (i.e., A⋂B ≠ Φ):
(ii) Agar set A aur set B mein kuch common element naa ho (i.e., A⋂B = Φ):
I hope ki mera ye article aap ko pasand aaya hoga. Agar aap ko mera ye article pasand aaya ho to comment karke hame bata sakte hain. Aapke dwaara kiye gaye comment se hame iss tarah ke post/article ko likne ke liye motivation milta hai.
Read Also:
THANKS FOR READING THIS BLOG.
Let's Begin...
Difference of Sets
Maan lijiye A aur B koi do(two) set hain. To A aur B ka Difference (in the same order) wo set hota hai jisme set A ke wo elements aate hain jo set B mein nahi aate hain. Hum set A aur set B ke Difference ko symbolically 'A - B' se show karte hain aur isko 'A minus B' padhte hain (read karte hain). Example ke liye, maan lijiye A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8} then
A - B = {1, 2, 3, 4, 5, 6} - {2, 4, 6, 8}
= {1, 3, 5}.
Isi tarah se B - A = {2, 4, 6, 8} - {1, 2, 3, 4, 5, 6}
= {8}.
[Note:
(i) Set A aur B, chaahe A aur B koi se bhi sets ho, ke Difference ko set-builder form mein aise define kiya jaata hai- A - B = {x:x ∈ A or x ∉ B}
(ii) A - B ko A\B se bhi denote kiya jaata hai].
Chaliye 'Difference of Sets' ko aur better tarike se samajhne ke liye kuch aur examples dekh lete hain.
Ex.1. A = {a, e, i, o, u} and B = {a, i, u}. Find A - B. And B - A also.
Solution: A = {a, e, i, o, u}
B = {a, i, u}
A - B = {a, e, i, o, u} - {a, i, u}
= {e, o}
B - A = {a, i, u} - {a, e, i, o, u}
= { }
= Φ
Ex.2. If A = {1}, B = {1, 2, 5} and C = {1, 2, 3, 6, 7} then find A - B, B - C and A - C.
Solution: A = {1}
B = {1, 2, 5}
C = {1, 2, 3, 6, 7}
A - B = {1} - {1, 2, 5}
= { }
= Φ
B - C = {1, 2, 5} - {1, 2, 3, 6, 7}
= {5}
C - A = {1, 2, 3, 6, 7} - {1}
= {2, 3, 6, 7}
Ex.3. If set P = {x:x is a natural number and 1 < x ≤ 6} and set Q = {x:x is a natural number and 6 < x < 10}. Find P - Q.
Solution: P = {x:x is a natural number and 1 < x ≤ 6}
= {1, 2, 3, 4, 5, 6}
Q = {x:x is a natural number and 6 < x < 10}
= {7, 8, 9}
P - Q = {1, 2, 3, 4, 5, 6} - {7, 8, 9}
= {1, 2, 3, 4, 5, 6}
= {x:x is a natural number and 1 ≤ x < 7}.
Venn Diagram for Difference of Sets
Kinhi do(two) sets, maan lijiye set A aur set B, ke liye A - B aur B - A ka Venn diagram kuch aisa hota hai-
For A - B:
(i) Agar set A aur set B mein kuch common element ho (i.e., A⋂B ≠ Φ):
 |
| Coloured part is A - B. |
(ii) Agar set A aur set B mein kuch common element naa ho (i.e., A⋂B = Φ):
 | |
|
For B - A:
(i) Agar set A aur set B mein kuch common element ho (i.e., A⋂B ≠ Φ):
 | |
|
(ii) Agar set A aur set B mein kuch common element naa ho (i.e., A⋂B = Φ):
 |
| Coloured part is B - A. |
I hope ki mera ye article aap ko pasand aaya hoga. Agar aap ko mera ye article pasand aaya ho to comment karke hame bata sakte hain. Aapke dwaara kiye gaye comment se hame iss tarah ke post/article ko likne ke liye motivation milta hai.
Read Also:
THANKS FOR READING THIS BLOG.
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