- #1
ice109
- 1,714
- 6
im just starting to work through vol 1 of apostol and these questions are kind of dumbfounding?
#3 on page 15
Let A={1}, B={1,2} Discuss the validity of the following statements (prove the ones that are true)
(a) [tex]A\subset B[/tex]
(b) [tex]A\subseteq B [/tex]
(c) [tex]A \in B[/tex]
(d) [tex] 1 \in A [/tex]
(e) [tex] 1 \subseteq B[/tex]
(f) [tex] 1 \subset B [/tex]
these are all obvious but what does he mean by prove? for (a) i have written: 1 is an element of A and an element of B but 2 is only an element of B hence A subeq B.
i don't know to how "prove" this stuff.
#7 on page 16
Prove the following properties of set equality.
(a){a,a}={a}
(b){a,b}={b,a}
(c){a}={b,c} iff a=b=c
the first two are just notational? the third follows from the first. these are all obvious but i don't know how to rigorously write it down.
#3 on page 15
Let A={1}, B={1,2} Discuss the validity of the following statements (prove the ones that are true)
(a) [tex]A\subset B[/tex]
(b) [tex]A\subseteq B [/tex]
(c) [tex]A \in B[/tex]
(d) [tex] 1 \in A [/tex]
(e) [tex] 1 \subseteq B[/tex]
(f) [tex] 1 \subset B [/tex]
these are all obvious but what does he mean by prove? for (a) i have written: 1 is an element of A and an element of B but 2 is only an element of B hence A subeq B.
i don't know to how "prove" this stuff.
#7 on page 16
Prove the following properties of set equality.
(a){a,a}={a}
(b){a,b}={b,a}
(c){a}={b,c} iff a=b=c
the first two are just notational? the third follows from the first. these are all obvious but i don't know how to rigorously write it down.