Let f : N −→ R and f(x) = √ 9x
The domain is all natural numbers: {0, 1, 2, 3, ...}
The codomain is all real numbers.
The range i believe is [0, +infinity)
I believe that although the above is a function since every input of x provides a output that fits in our codomain. I also believe that...
So a empty set is a subset of any set making d true. For e since its asking if the empty set element can be found in {φ, {φ}} as the set does indeed contain a empty set. making it true as well.
So far I have determined that first two statements are true but really need help on understanding proper logic as I don't think I am doing it right.
1 State whether the following are True or False
a.) {{φ}} ∈ {{φ}, {φ}}
b.) {φ} ∈ {{φ}, {φ}}
c.) {{φ}} ⊆ {φ, {φ}}
d.) φ ⊆ {φ, {φ}}
e.) φ ∈...