Predicate logic formulas without quantifiers can be verified using derivation. But when it comes to first order logic (predicate logic with quantifiers), the simplest way is to apply logical reasoning. Most of these questions asked will be for very small formulas and we can easily apply logical reasoning to check if they are valid. The […]

# Engineering Mathematics

## Number of Binary trees possible with n nodes

What is the no. of distinct binary trees possible with n labeled nodes? Solution $ \frac{(2n)!} { (n+1)!}$ (Proof to be Added) What is the no. of distinct binary trees possible with n unlabeled nodes? (No. of structurally different binary trees possible with n nodes) Solution If the nodes are similar (unlabeled), then the no. […]

## Calculus

Materials for GATE preparation in Calculus

## Linear Algebra

Materials for GATE preparation in Linear Algebra

## Graph Theory

Materials for GATE preparation in Graph Theory