Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample. If Upper P (Upper E )plus Upper P (Upper F )equals Upper P (Upper E union Upper F )plus Upper P (Upper E intersect Upper F ), then E and F are mutually exclusive events.

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Step-by-step explanation:

Given the statement

If , then E and F are mutually exclusive events.

If two events are mutually exclusive, they have no elements in common. Thus, P(E∩F)=0.

Therefore, the statement is always true as P(E∩F)=0

For mutually exclusive events:

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  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.