Trivial topology

(See attached file for full problem description with all symbols) --- Let X and Y be topological spaces, where the only open sets of Y are the empty set and Y itself, i.e., Y has the trivial topology • Show that any map is continuous • Show that Y is path connected and simply connected. ---

Sets and Functions (I): Sets and Set Inclusion: Let U be the single-element set { 1 }. There are two subsets, the empty set φ and { 1 } itself. If A and B are arbitrary subsets of U, there are four possible relations of the form “A is subset of B”. Count the number of true relations among these.

Topology Sets and Functions (I) Sets and Set Inclusion Let U be the single-element set { 1 }. There are two subsets, the empty set φ and { 1 } itself. If A and B are arbitrary subsets of U, there are four possible relations of the form "A is subset of B". Count the number of true relations among these.

Sets and Functions (II): Sets and Set Inclusion: Let U be the set { 1, 2 }. There are four subsets . List them. If A and B are arbitrary subsets of U, there are 16 possible relations of the form “A is subset of B”. Count the number of true ones.

Topology Sets and Functions (II) Sets and Set Inclusion Let U be the set { 1, 2 }. There are four subsets . List them. If A and B are arbitrary subsets of U, there are 16 possible relations of the form "A is subset of B". Count the number of true ones.

Trigonometry and Bearings

A boat travels in a direction of N40(deg) E for 3 hours at 20 mph. How far North and how far East did the boat travel?

A tree cast a shadow 86 ft long when the angle of elevation of the sun is 48.7 degree. find the height of the tree.

A tree cast a shadow 86 ft long when the angle of elevation of the sun is 48.7 degree. find the height of the tree.