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Verify (A \cap B)^{\prime} = A^{\prime} \cup B^{\prime} using Venn diagram.
 
L.H.S: (A \cap B)^{\prime}
 
LHS_(ANB)'.svg
 
R.H.S: A^{\prime} \cup B^{\prime}
 
RHS_A_pri U_B_pri.svg
 
Therefore, (A \cap B)^{\prime} = A^{\prime} \cup B^{\prime}.