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reflexive property of congruence
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Is intersection of two topologies on X a topology on X?
A topology is a set of elements or subsets that follows these properties:∅ and X belongs to the setAny union of the subsets belongs to the set.Any intersection of the subsets belongs to the set.Yes, any intersection of two topologies on X is always a topology on X. Consider this example:Let X = {1,2,3}, T = {∅, {1},{2},{1,2},X} and S = {∅, {1}, {3}, {1,3},X}Then, S ∩ T = {∅, X, {1}}To show that S ∩ T is a topology, we need to prove these properties:∅ and X belongs to the setAny union of the subsets belongs to the set.Any intersection of the subsets belongs to the set.Step 1: Prove the first property is followedSince the empty set and X belongs to S ∩ T, the first property is followed. That is obvious. ;)Step 2: Prove the second property is followedSelect any union of any pair of subsets. You should see that this property is also satisfied. How?∅ U X = X ∈ S ∩ T∅ U {1} = {1} ∈ S ∩ T{1} U X = X ∈ S ∩ TStep 3: Prove the third property is followedAny intersection of the subsets belong to the set obviously. See below:∅ ∩ X = ∅ ∈ S ∩ T∅ ∩ {1} = ∅ ∈ S ∩ T{1} ∩ X = {1} ∈ S ∩ TSo the intersection of two topologies on X is a topology.
what- If you are given or can prove that two triangles are congruent, then you may use CPCTC to prove that the angles or sides are?
congruent
What property of multiplication do you use to rename fractions?
Identity property of multiplication
What property can you use to find the missing number for 10x equals 0?
You would use the Property Of Zero
P-q and q-p are logically equivalent prove?
p --> q and q --> p are not equivalent p --> q and q --> (not)p are equivalent The truth table shows this. pq p --> q q -->(not)p f f t t f t t t t f f f t t t t
