User 123

35 votes

12 answers

81k views

Is $[p \land (p \to q)] \to q$ a tautology?

asked Jan 13, 2016 at 21:28

3 votes

1 answer

2k views

Find a False Counterexample for : "$\forall$ $A, B$ and $C$, we have $A \cap (B - C) = (A \cap B) - (A \cap C)$"

asked Jan 28, 2016 at 21:52

3 votes

3 answers

1k views

Simplify $(k +1)! > (k + 1)^2$ to prove true for $k ≥ 4$

asked Feb 5, 2016 at 18:34

3 votes

1 answer

55 views

What is $25^k$ + $5^k$ [closed]

asked Feb 5, 2016 at 0:26

2 votes

2 answers

2k views

Simple expression for $\sum_{k=1}^{n-1}\:\frac{1}{k\left(k+1\right)}$

asked Feb 8, 2016 at 20:48

2 votes

3 answers

611 views

Can I further simplify $5^k \cdot 5 + 9 < 6^k \cdot 6$ to prove this is true

asked Feb 5, 2016 at 18:14

2 votes

2 answers

36 views

If $B= \{1, 2\}$ and $C = \{\{1,2\}\}$ what is $B \times C$?

asked Feb 1, 2016 at 17:56

2 votes

1 answer

8k views

Prove for all integers n such that n ≥ 3, $ 4^3 + 4^4 + 4^5 … 4^n = \frac{4(4^n - 16)}{3}$

asked Feb 4, 2016 at 22:29

2 votes

2 answers

6k views

Is this a valid proof of "a, b are rational, b ≠ 0, r is irrational, then a + br is irrational"

asked Jan 19, 2016 at 18:50

2 votes

2 answers

9k views

Is this a valid proof of "For all integers m and n, if mn is even, then m is even, or n is even"?

asked Jan 19, 2016 at 20:33

1 vote

5 answers

13k views

How to raise a fraction to a fractional exponent?

asked Nov 23, 2015 at 19:56

1 vote

3 answers

105 views

Is 'Some of x are true' a negation of 'All of x are true'?

asked Jan 14, 2016 at 19:25

1 vote

2 answers

7k views

Is a graph with four vertices of degrees 1, 2, 3, and 3 possible?

asked Mar 10, 2016 at 17:01

1 vote

1 answer

1k views

Prove T(n) = nlgn for recurrence T(n) = 2T(n/2) + n for 2^k k > 0 and T(n) = 2 for n = 2

asked Oct 1, 2016 at 14:29

1 vote

1 answer

4k views

How many integers from 1 through 100 are neither multiples of 2 nor multiples of 9?

asked Feb 26, 2016 at 16:18

1 vote

1 answer

820 views

Explicit formula for $d_k = 5d_{k−1} + 2$, for all integers $k ≥ 1$ $d_0 = 2$

asked Feb 26, 2016 at 16:48

0 votes

2 answers

167 views

r-combinations with repetition allowed - How to calculate $X_{\geq y}$?

asked Feb 26, 2016 at 18:42

0 votes

2 answers

6k views

How many distinguishable ways can the letters of the word MATHEMATICS be arranged in order? [duplicate]

asked Mar 3, 2016 at 16:30

0 votes

1 answer

847 views

How many permutations of the letters TRIANGLE contain A, N and G not to be together ?

asked Mar 3, 2016 at 16:54

0 votes

2 answers

42 views

Bag has 30 reds, yellows, and greens - How many combos of 10 have at most 3 yellow?

asked Mar 3, 2016 at 17:33

0 votes

4 answers

4k views

Prove $n^3 + 7n + 3$ is divisible by 3 for all integers n ≥ 0

asked Feb 5, 2016 at 17:41

0 votes

1 answer

42 views

Does $2^{k+1} = 2^k * 2^1$?

asked Feb 5, 2016 at 18:01

0 votes

1 answer

115 views

Prove/Disprove - If $f_1(n) = O(g_1(n))$ and $f_2(n) = O(g_2(n))$, then $f_1(n) + f_2(n) = O(g_1(n)+g_2(n))$

asked Sep 29, 2016 at 14:15

0 votes

3 answers

3k views

Explicit formula for $e_k = 4e_{k-1} + 5$

asked Feb 10, 2016 at 20:43

0 votes

2 answers

2k views

Let A ={x ∈ Z | x =18a − 2 for some integer a } and B ={y ∈ Z | y = 18b + 16 for some integer b} Prove A ⊆ B

asked Feb 1, 2016 at 18:36

0 votes

1 answer

2k views

Any collection of n coins can be obtained using a combination of 3¢ and 5¢ coins where n ≥ 14

asked Feb 7, 2016 at 20:37

0 votes

2 answers

230 views

Finding the complement of a set

asked Feb 8, 2016 at 20:04

0 votes

1 answer

49 views

Further simplifying this logical equivalence

asked Jan 6, 2016 at 20:54

0 votes

2 answers

669 views

How can I further simplify (P ∨ ¬Q) → ¬(P ∨ Q)?

asked Jan 14, 2016 at 18:15

0 votes

2 answers

763 views

What is the contrapositive of "if $x^2 (y + 3)$ is even, then $x$ is even or $y$ is odd"?

asked Jan 23, 2016 at 20:37

Stack Exchange Network

34 Questions

Is $[p \land (p \to q)] \to q$ a tautology?

Find a False Counterexample for : "$\forall$ $A, B$ and $C$, we have $A \cap (B - C) = (A \cap B) - (A \cap C)$"

Simplify $(k +1)! > (k + 1)^2$ to prove true for $k ≥ 4$

What is $25^k$ + $5^k$ [closed]

Simple expression for $\sum_{k=1}^{n-1}\:\frac{1}{k\left(k+1\right)}$

Can I further simplify $5^k \cdot 5 + 9 < 6^k \cdot 6$ to prove this is true

If $B= \{1, 2\}$ and $C = \{\{1,2\}\}$ what is $B \times C$?

Prove for all integers n such that n ≥ 3, $ 4^3 + 4^4 + 4^5 … 4^n = \frac{4(4^n - 16)}{3}$

Is this a valid proof of "a, b are rational, b ≠ 0, r is irrational, then a + br is irrational"

Is this a valid proof of "For all integers m and n, if mn is even, then m is even, or n is even"?

How to raise a fraction to a fractional exponent?

Is 'Some of x are true' a negation of 'All of x are true'?

Is a graph with four vertices of degrees 1, 2, 3, and 3 possible?

Prove T(n) = nlgn for recurrence T(n) = 2T(n/2) + n for 2^k k > 0 and T(n) = 2 for n = 2

How many integers from 1 through 100 are neither multiples of 2 nor multiples of 9?

Explicit formula for $d_k = 5d_{k−1} + 2$, for all integers $k ≥ 1$ $d_0 = 2$

r-combinations with repetition allowed - How to calculate $X_{\geq y}$?

How many distinguishable ways can the letters of the word MATHEMATICS be arranged in order? [duplicate]

How many permutations of the letters TRIANGLE contain A, N and G not to be together ?

Bag has 30 reds, yellows, and greens - How many combos of 10 have at most 3 yellow?

Prove $n^3 + 7n + 3$ is divisible by 3 for all integers n ≥ 0

Does $2^{k+1} = 2^k * 2^1$?

Prove/Disprove - If $f_1(n) = O(g_1(n))$ and $f_2(n) = O(g_2(n))$, then $f_1(n) + f_2(n) = O(g_1(n)+g_2(n))$

Explicit formula for $e_k = 4e_{k-1} + 5$

Let A ={x ∈ Z | x =18a − 2 for some integer a } and B ={y ∈ Z | y = 18b + 16 for some integer b} Prove A ⊆ B

Any collection of n coins can be obtained using a combination of 3¢ and 5¢ coins where n ≥ 14

Finding the complement of a set

Further simplifying this logical equivalence

How can I further simplify (P ∨ ¬Q) → ¬(P ∨ Q)?

What is the contrapositive of "if $x^2 (y + 3)$ is even, then $x$ is even or $y$ is odd"?