Hrm/531 Week 9 Quiz
Definition Let G be a under binary operation * and H be a subset of G is called a subgroup of G if H also forms a group under the operation *.It is denoted by H≤G, read as “H is a subgroup of G”. Definition
Let G be a group. A fuzzy subset μ of G is called a fuzzy subgroup if for all x,y∈G, μ(xy)≥ min{μ(x),μ(y)} μ(x^(-1)) = μ(x) Definition
A Q-fuzzy set μ is called a Q-fuzzy subgroup of a group G, if for x,y∈G,q∈Q, μ(xy,q)≥ min{μ(x,q),μ(y,q)} μ(x^(-1),q) = μ(x,q)
1.8 Definition
A subgroup H of a group G is normal in G if and only if gH=Hg for all g in G, i.e., the sets of left and right cosets coincide.
Let G be a group. A fuzzy subset μ of G is called a fuzzy subgroup if for all x,y∈G, μ(xy)≥ min{μ(x),μ(y)} μ(x^(-1)) = μ(x) Definition
A Q-fuzzy set μ is called a Q-fuzzy subgroup of a group G, if for x,y∈G,q∈Q, μ(xy,q)≥ min{μ(x,q),μ(y,q)} μ(x^(-1),q) = μ(x,q)
1.8 Definition
A subgroup H of a group G is normal in G if and only if gH=Hg for all g in G, i.e., the sets of left and right cosets coincide.