Prove or disprove that the intersection of any collection
ofclosed sets is closed.

Intersection of collection of any closed set is a closed set.    

Step-by-step explanation:

Let F be a collection of arbitrary closed sets and let be closed set belonging to F.

We define a closed set as the set that contains its limit point or in other words it can be described that the complement or not of a closed set is an open set.

Thus, we can write R as

Now, applying De-Morgan's Theorem, we have

Since we knew are closed set, thus, is an open set.

We also know that union of all open set is an open set.

Thus, is an open set.

Thus, R is a closed set.

Hence, the theorem.  

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

step-by-step explanation:

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