Question 1094176
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A is some event while A^c is the complement of said event. 


What this means is that if event A doesn't happen, then surely A^c will happen. 
The same can be said in reverse: If A^c doesn't happen then event A will happen. 


These two events are completely opposite in nature. 
So P(A and A^c) = 0 because it's impossible to have BOTH happen at the same time. 
<font color=red>So choice A is true making choice B to be false. </font>


Similarly, P(A or A^c) = 1 because either one or the other must happen, giving us 100% certainty of this compound event. 
<font color=red>That makes choice D true and choice C false. </font>
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