Recent content by SamitC

It seems I can't use the blanks. If the last two digits are blank then it means 6 character password which is already counted. Now, 7th or 8th char being blank means the same thing - 7 character password. Now I am asking to myself - can we solve this problem using the blanks as characters with...

Can you pls. explain more on this? I did not understand the blank+letter or letter+blank concept. As per my understanding, blank is nothing. So if two blanks remain anywhere in a 7 character word, it becomes a 5 character word. i.e. does not matter where blank remains but what matters is how...

Problem: How many passwords can be created with 6 to 8 characters. Letter case does not matter. Every password must have at least 1 digit. Approach taken in the solution in the book: Passwords with 6 characters P6 = 36^6 − 26^6 = 1,867,866,560. Similarly, we have P7 = 36^7 − 26^7 =...

Thanks.

Suppose there are numbers 1, 2, 3, 4, 5, 6, 7, 8. Question is: How many ways can we pick 4 non adjacent numbers (order does not matter)? Now, as per formula it is C(n-r+1,r) = C(8-4+1,4) = C(5,4)=5. Crosschecking, I could find only four: 1,3,5,7 : 1,3,5,8 : 1,4,6,8 : 2,4,6,8 Not...

I am studying maths out of hobby. I feel sometimes that I can not move ahead because I get stuck with tough problems. Even after I move ahead, when i come back after quite some time, i get stuck with the same problems. Sometimes it is frustrating. And my interest and attention levels are going...

Hi, Thanks for your reply. Now i am confused with another example: Suppose L (x,y) means "x loves y". Now to write "There is someone who loves no one besides himself or herself". The answer in the book is: ∃x ∀y {L(x,y) ↔ x = y}] Here what is the need for the Bi-conditional or backward...

The problem statement: Suppose P(x). And if I want to write "For exactly one x, P(x) then: If we write ∃x [P(x) ∧ ∀y {P(y) → x = y}]. This is as per answer in the books. Now, suppose P(y) is false. It will still mean x = y. Shouldn't it be ∃x [P(x) ∧ ∀y {P(y) ↔ x = y}] Same problem with ∃x...

Thank you.

Hello, Suppose a problem statement is : In a school, suppose S(x) is “x is a student”, F(x) is “x is a faculty member” and A (x, y) is “x asked a question to y”. Domain is all the people associated with the school. Write the following using quantifiers: "Some student did not ask any faculty...

Thanks for your reply. Sorry...don't know why i asked this question... a (s/b) = c ...i don't know why I was thinking the other way. Anyways...thanks

Hi, One silly thing is bothering me. As per one lemma, If a, b, and c are positive integers such that gcd(a, b) = 1 and a | bc, then a | c. This is intuitively obvious. i.e. Since GCD is 1 'a' does not divide 'b'. Now, 'a' divides 'bc' so, 'a' divides 'c'. Proved. What is bothering me is ...

The function part made it clear. Thanks.

Hello, This is a very basic question but bothering me on some exercises. , Then how is the range of y is ? What if x is 0, then we can have y = 1 or y = -1. While doing some exercises I encountered this issue and can't match the answers. Thanks in advance

How can I show (without using truth table) that p → q is equivalent to F ↓ ((F ↓ p) ↓ q) where F is constant "false" and p and q are propositions? Is it possible to have a similar kind of expression with T (true) instead of F? Thanks in advance!