Question

For cach set below, determine if it's countable, or uncountable. Justify your claims.

(a) A={x∈Z∣x is not divisible by 3}.
(b) B=Q∩(−1,1).
(c) C=(−1,1)ᶜ (here U=R is the universal set.
(d) D=P(E), where E is the sct of even integers.
(e) F=(−1,1)∪Q.

Answer 1

The questions explore set theory in terms of countable and uncountable sets and probabilities related to dice games, focusing on mutual exclusivity and event independence.

Step-by-step explanation:

The questions provided involve the determination of whether given sets are countable or uncountable, calculation of probabilities in dice rolling scenarios, and the exploration of set relationships like whether sets are mutually exclusive or independent. The importance of these distinctions lies in understanding the nature of infinity in the case of countable vs. uncountable sets and the behavior of events in probability theory to predict outcomes and assess the relationships between events.