Closure Property
A non-empty set z is closed under a binary operation, * if for all a, b € Z.
Example: A binary operation * is defined on the set S= {0, 1, 2, 3, 4} by X*Y = x+y-xy. Find (a)2*4 (b)3*1 (c)0*3. Is the set S closed under the operation *?
Solution
(a)2*4, i.e, x = 2, y = 4
2+4 - (2x4) = 6-8 = -2
(b)3*1 = 3 + 1 - (3x1) = 4 - 3 =1
(c)0*3 = 0 + 3 - (0x3) = 3
Since -2€ S, therefore the operation * is not closed in S.
A non-empty set z is closed under a binary operation, * if for all a, b € Z.
Example: A binary operation * is defined on the set S= {0, 1, 2, 3, 4} by X*Y = x+y-xy. Find (a)2*4 (b)3*1 (c)0*3. Is the set S closed under the operation *?
Solution
(a)2*4, i.e, x = 2, y = 4
2+4 - (2x4) = 6-8 = -2
(b)3*1 = 3 + 1 - (3x1) = 4 - 3 =1
(c)0*3 = 0 + 3 - (0x3) = 3
Since -2€ S, therefore the operation * is not closed in S.
Closure Property
A non-empty set z is closed under a binary operation, * if for all a, b € Z.
Example: A binary operation * is defined on the set S= {0, 1, 2, 3, 4} by X*Y = x+y-xy. Find (a)2*4 (b)3*1 (c)0*3. Is the set S closed under the operation *?
Solution
(a)2*4, i.e, x = 2, y = 4
2+4 - (2x4) = 6-8 = -2
(b)3*1 = 3 + 1 - (3x1) = 4 - 3 =1
(c)0*3 = 0 + 3 - (0x3) = 3
Since -2€ S, therefore the operation * is not closed in S.
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