7. Let A = The set of all natural numbers less than 8, B = The set of all prime number
less than 8, C = The set of even prime number. Verify that
(i) (AN B)xC = (AⓇC) n(BXC) (ii) A x(B-C)= (A x B) - (AXC)
Answers
Answer:
(A∩B)xC=(AxC)∩(BxC)
A x(B-C)= (AxB) - (AxC)
Step-by-step explanation:
To verify:
1.(A∩B)xC=(AxC)∩(BxC)
2.A x(B-C)= (AxB) - (AxC)
Given:
A={1,2,3,4,5,6,7}
B={2,3,5,7}
C={2}
1.
A∩B ={2,3,5,7}
(A∩B)xC={ (2,2), (3,2), (5,2), (7,2) }...(1)
AxC={(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2)}
BxC= { (2,2), (3,2), (5,2), (7,2) }
(AxC)∩(BxC)= { (2,2), (3,2), (5,2), (7,2) }...(2)
From (1) and (2)
(A∩B)xC=(AxC)∩(BxC)
2.
B-C={3, 5, 7}
A x(B-C)={ (1,3),(1,5),(1,7),(2,3),(2,5),(2,7),(3,3),(3,5),(3,7),(4,3),(4,5),(4,7),(5,3),(5,5),(5,7),(6,3),(6,5),(6,7),(7,3),(7,5),(7,7)}....(3)
AxB={ (1,2),(1,3),(1,5),(1,7),(2,2),(2,3),(2,5),(2,7),(3,2),(3,3),(3,5),(3,7),(4,2),(4,3),(4,5),(4,7),(5,2),(5,3),(5,5),(5,7),(6,2),(6,3),(6,5),(6,7),(7,2),(7,3),(7,5),(7,7)}
AxC={(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2)}
(AxB) - (AxC)= { (1,3),(1,5),(1,7),(2,3),(2,5),(2,7),(3,3),(3,5),(3,7),(4,3),(4,5),(4,7),(5,3),(5,5),(5,7),(6,3),(6,5),(6,7),(7,3),(7,5),(7,7)}.........(4)
From (3) and (4)
A x(B-C)= (AxB) - (AxC)
Answer:
1.(A∩B)xC=(AxC)∩(BxC)
2.A x(B-C)= (AxB) - (AxC)
Step-by-step explanation:
To verify:
1.(A∩B)xC=(AxC)∩(BxC)
2.A x(B-C)= (AxB) - (AxC)
Given:
A={1,2,3,4,5,6,7}
B={2,3,5,7}
C={2}
1.
A∩B ={2,3,5,7}
(A∩B)xC={ (2,2), (3,2), (5,2), (7,2) }...(1)
AxC={(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2)}
BxC= { (2,2), (3,2), (5,2), (7,2) }
(AxC)∩(BxC)= { (2,2), (3,2), (5,2), (7,2) }...(2)
From (1) and (2)
(A∩B)xC=(AxC)∩(BxC)
2.
B-C={3, 5, 7}
A x(B-C)={ (1,3),(1,5),(1,7),(2,3),(2,5),(2,7),(3,3),(3,5),(3,7),(4,3),(4,5),(4,7),(5,3),(5,5),(5,7),(6,3),(6,5),(6,7),(7,3),(7,5),(7,7)}....(3)
AxB={ (1,2),(1,3),(1,5),(1,7),(2,2),(2,3),(2,5),(2,7),(3,2),(3,3),(3,5),(3,7),(4,2),(4,3),(4,5),(4,7),(5,2),(5,3),(5,5),(5,7),(6,2),(6,3),(6,5),(6,7),(7,2),(7,3),(7,5),(7,7)}
AxC={(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2)}
(AxB) - (AxC)= { (1,3),(1,5),(1,7),(2,3),(2,5),(2,7),(3,3),(3,5),(3,7),(4,3),(4,5),(4,7),(5,3),(5,5),(5,7),(6,3),(6,5),(6,7),(7,3),(7,5),(7,7)}.........(4)
From (3) and (4)
A x(B-C)= (AxB) - (AxC)