Answer to Question #125567 in Discrete Mathematics for kavee

Question #125567
(a) Use a Venn diagram to illustrate the relationships A ⊆ B and B ⊆ C.
(b) Use a Venn diagram to illustrate the relationships A ⊂ B and B ⊂ C.
(c) Use a Venn diagram to illustrate the relationships A ⊂ B and A ⊂ C.
(d) Suppose that A , B, and C are sets such that A ⊆ B and B ⊆ C. Show that A ⊆ C.
(e) Find two sets A and B such that A ∈ B and A ⊆ B.
1
Expert's answer
2020-07-13T20:00:40-0400


D)


A\subset B, x\in A\to x\isinB,

B\subsetC, x\isin B\to x\isin C.


So for a particular X,x\isin A\to x\isin B AND x\isin B\to X\in C

By the transitivity of implication

this means that x\isin A \to x\isin C

So A is subset of C.


E)A={} or \emptyset and B={\emptyset ,{1}}


A\subset B,we can easily see that {} is an empty set which is a subset of B.


A\isin B,since we can easily see that \emptyset is an element of B.



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