Prove the following:-
1space space 1. space space B subset of A union B 2. space A intersection B subset of B 3. space B subset of A left right double arrow A intersection B equals B 4. space A subset of C space a n d space B subset of D rightwards double arrow A union B subset of C union D 5. B subset of C rightwards double arrow A intersection B subset of A intersection C 6. space A equals B left right double arrow A subset of B space a n d space B subset of A space space 1. space space B subset of A union B 2. space A intersection B subset of B 3. space B subset of A left right double arrow A intersection B equals B 4. space A subset of C space a n d space B subset of D rightwards double arrow A union B subset of C union D 5. B subset of C rightwards double arrow A intersection B subset of A intersection C 6. space A equals B left right double arrow A subset of B space a n d space B subset of A space space 1. space space B subset of A union B 2. space A intersection B subset of B 3. space B subset of A left right double arrow A intersection B equals B 4. space A subset of C space a n d space B subset of D rightwards double arrow A union B subset of C union D 5. B subset of C rightwards double arrow A intersection B subset of A intersection C 6. space A equals B left right double arrow A subset of B space a n d space B subset of A

Asked by ravikantmanchanda | 20th May, 2015, 10:01: PM

Expert Answer:

left parenthesis i right parenthesis C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma space t h e space c o l o u r space o f space B space i n space A union B space a n d space B space s e p a r a t e l y space a r e space s a m e. space H e n c e space w e space c a n space d e d u c e space t h a t space B subset of A union B. space
 
left parenthesis i i right parenthesis C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma space t h e space c o l o u r space o f space A intersection B space a n d space B space s e p a r a t e l y space a r e space s a m e. space H e n c e space w e space c a n space d e d u c e space t h a t space A intersection B subset of B. space
 
 
left parenthesis i i i right parenthesis C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma space B subset of A F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma space t h e space c o l o u r space o f space A intersection B space a n d space B space s e p a r a t e l y space a r e space s a m e. space H e n c e space w e space c a n space d e d u c e space t h a t space A intersection B equals B. space
 
left parenthesis i v right parenthesis C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma space open parentheses A union B close parentheses subset of open parentheses C union D close parentheses.
left parenthesis v right parenthesis C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma space open parentheses A intersection B close parentheses subset of open parentheses C intersection D close parentheses.
 
left parenthesis v i right parenthesis C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
F r o m space t h e space f i g u r e comma space i t space i s space c l e a r space t h a t comma space A equals B space a n d space A subset of B space a n d space B subset of A.
 
 

Answered by Vimala Ramamurthy | 22nd May, 2015, 11:08: AM