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(1) Use inductive reasoning to predict the next number in each list.
(a) 1, 4, 9, 16, 25, 36, 49, ?
(b) 2, 7, −3, 2, −8, −3, −13, −8, −18, ?
(c) 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, ?
(a) 1, 4, 9, 16, 25, 36, 49, ?
(b) 2, 7, Ã ¢ 3, 2, Ã ¢ 8, Ã ¢ 3, Ã ¢ 13, Ã ¢ 8, Ã ¢ 18, ?
(c) 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, ?
(2) Find a pair of numbers that provides a counterexample to show that the given statement is false.
(a) If the sum of two counting numbers is an even counting number, then the product of the two counting numbers is an even
counting number.
(b) If the product of two counting numbers is an even counting
number, then both of the counting numbers are even counting
numbers.
(1) Use inductive reasoning to predict the next number in each list.
(a) 1, 4, 9, 16, 25, 36, 49, ?
(b) 2, 7, −3, 2, −8, −3, −13, −8, −18, ?
(c) 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, ?
(2) Find a pair of numbers that provides a counterexample to show that the given statement is false.
(a) If the sum of two counting numbers is an even counting number, then the product of the two counting numbers is an even
counting number.
(b) If the product of two counting numbers is an even counting
number, then both of the counting numbers are even counting
numbers.
(3) Use deductive reasoning to show that the following procedure always produces a number that is equal to the original number.
Procedure: Pick a number. Multiply the number by 6 and add 8.
Divide the sum by 2, subtract twice the original number,
and subtract 4.
If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area. *
r→ q ↔ ¬p
What is the value of x after each of these statements
a. if x+2=3 then x:=x + 1
b. if (x+1=3) OR (2x+2=3) then x:=x+1
c. if (2x +3=5) AND (3x +4= 7) then x= x + 1
d. if (x+1=2) XOR (x+2=3) then x:=x+1
e. if x < 2 then x:=x + 1
M is a subset of the set of natural numbers. 10 elements of the set are prime numbers, and the rest are divisible by either 2, or 3, or 5. Determine the cardinality of the set if it contains: 70 numbers that are divisible by 2; 60 numbers divisible by 3; 80 divisible by 5; 98 multiples by 2 or by 3; 95 multiples by 2 or by 5; 102 multiples by 3 or by 5; 20 numbers divisible by 30
prove that AUB = AU(B\A)
The sum of the first n positive odd integers is n2.
Establish the formula for the sum of the first n positive even integers and use proof by mathematical induction to prove its correctness.
Use predicates, quantifiers, logical connectives, and mathematical operators to express the statement that “Every positive integer is the sum of the squares of four integers.
Given set A = {A, B, C, D, E, F, G, H} and B = {B, D, E, J, K}. Find for the:
1. A ∪ B
2. A ∩ B
3. A x B
4. B x A
#340153 on Dec 2023