Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$,  $ P ( B )=0.4$,  $P ( A \cap B )=0.8$

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$P ( A )=0.5$,  $P ( B )=0.4$,  $P (A \cup B)=0.8$

It is known that if $E$ and $F$ are two events such that $E \subset F,$ then $P ( E ) \leq P ( F )$

Here, it is seen that $P (A \cup B)> P ( A )$ and $P (A \cup B)> P ( B )$

Hence, $P(A)$ and $P(B)$ are consistently defined.

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