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Can anyone help me with this problem?

Given:

$A = \{a,b,c\}$

$G=I_A \cup\{(a,b), (b,a),(b,c),(c,b)\}$

$H=I_A \cup\{(b,c), (c,b)\}$ (Note: H is a refinement of G)

Then:

$A|G = \{G_a, G_b,G_c\}$ wherein $G_a = \{a,b\}, G_b=\{a,b,c\}, G_c=\{c,b\}$

$A|H = \{H_a,H_b,H_c\}$ wherein $H_a = \{a\}, H_b=\{b,c\}, H_c=\{b,c\}$

Is $G|H = A|H = \{H_a,H_b,H_c\}$ ?

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