How to construct the truth table of p or q ?
Q. 4: Construct the truth table of p or q Answer : Let p and q be any propositions then p or q is written as p ∨ q Step…
How to construct the truth table of p and q ?
Q. 3 : Construct the truth table of p and q P ∧ Q Answer : Let p and q be any propositions then p and q is written as…
How to construct the truth table of negation of p implies q or r ?
Q.(2) : Construct the truth table of negation of p implies q or r ¬p → (q ∨ r) Answer : Let any three propositions be P, Q and R…
Construct the truth table of p implies not q
Q.(1) : Construct the truth table of p implies not q Answer : Let a proposition p and another proposition q then p implies not q is written as p…
How to find eigen values of 4 by 4 matrix ?
Problem : How to find eigen values of 4 by 4 matrix ? Answer : For the given matrix\[A=\left(\begin{matrix}2&0&1&1\\1&2&5&-5\\0&0&3&0\\0&0&1&3\\\end{matrix}\right)\]Eigen values :Eigen values k of the matrix A are calculated by…
how to use Synthetic Division Method to solve 2x^4-15x^3+35x^2-30x+8=0
Question : Use Synthetic Division Method to solve 2x^4-15x^3+35x^2-30x+8=0 Solution : To solve the equation 2x^4-15x^3+35x^2-30x+8=0 \[ 2x^4-15x^3+35x^2-30x+8=0 \] (1) Since 2*1^4-15*1^3+35*1^2-30*1+8=2-15+35-30+8=45-45=0 Therefore x =1 is the root of the…
how to Apply mathematical induction method to prove
Question : Apply mathematical induction method to prove 1.1!+2.2!+3.3!+….+n.(n+1)!=(n+1)!-1 Answer : Proof by mathematical induction method Let the statement as [P_n:\ 1\cdot1!+2\cdot2!+3\cdot3!+…+n\cdot n!] Base Step : n=1 1.1!=2!-1 =>1=2-1 =>1=1…
Which one of the following is the closed form for the generating function of the sequence {an } defined below?
Question : Which one of the following is the closed form for the generating function of the sequence {an } defined below? if n is odd \[a_n =n+1 \] otherwise…
what is the value of the following limit
Question : what is the value of the following limit The value of the following limit is \[{\rm limit}_{x\rightarrow0}\frac{\sqrt x}{1-e^{2\sqrt x}}\] Sol: Let the limit as \[L={\rm limit}_{x\rightarrow0+}\frac{\sqrt x}{1-e^{2\sqrt x}}\]…
how to find greatest common divisor of 1760 and 803 by Euclidean algorithm
Question : Find greatest common divisor of 1760 and 803 by Euclidean algorithm Solution : Euclidean Algorithm states that If a > b > 0 and a = bq +…