Weak Induction (1) Using weak induction, prove that 3" < n! for all integers n > 6.
(2) Prove that log(n!) < n log(n) for all integers n > 1.
Reminder 1: log(1) = 0.
Reminder 2: log(a*b) = log(a) + log (6).
Reminder 3: If a < b then log(a) < log(6).
Note: The base of the logarithms doesn't matter for any of the above.
(3) Prove for all integers n > 1 that if A1, A2, ..., An and B are sets, then:.
(A1∩A2∩...∩An)UB = (A1UB)∩(A2UB)∩...∩(AnUB)
Hint: Use the fact that (XNY) UZ = (XUZ)n(Y UZ) where X, Y, and Z are sets.

Following are the answer to this question:

Explanation:

In option 1:

The value of n is= 7, which is (base case)

when n=k for the true condition:

when n=k+1 it tests the value:

since k>6  hence the value is KH>3 hence proved.

In option 2:

when:

for n=1:(base case)

0<=0 \\ condition is true

when the above statement holds value n=1

when n=k

when n=k+1

In option 3:

when n=1:

when n=k

hence n=k+1 is true.

i do believe its (c); they are required to perform any summarization or redistribution tasks

explanation:

given the lack of choices, i'm gonna wing it and say that pushing your car off a cliff might not be the best idea. your car might sustain damage from the fall and will probably result in the car being too damaged to jump start.

if that's not good enough, avoid filling the car with bees. bees might get agitated when trapped or during the moving process, and might result in death or painful stings that will make jump starting your car very difficult. but in the event that you do choose to fill your car with bees, remember to wear protective gear!