Prove that {V, ^, +} is not an adequate set of connectives.

Problem 6. Let ? = {?, ?, ?, ?}. Define ? on ? as follows: ? = {(?, ?), (?, ?), (?, ?), (?, ?), (?, ?)}. (b) Find the symmetric closure of R.

Implement the stack ADT in a fully generic manner using the STL vectorclass.

Write it in Racket Define a function (bst? n) to test for membership to determine if a collection of nodes satisfies the bst property (is a bst). The BST property is that for any node n in the bst: all nodes to left must have value < (node-value n) all nodes to right must have value > (node-value n) Skeleton for function (define (bst? n) (cond )) The function can be defined as one big conditional with multiple cases. Some of the cases are base cases, others will require a recursive call to bst? There is more than one way to develop the cases, but here are some starting point ideas. If n is null or empty, result is true #t else if n is not a node structure, then result is false #f else if n has no child nodes, then result is true #t else if n has one child on the left, then result is n.left.value < n.value AND bst?(n.left) is true else if n has one child on the right, then result is n.right.value > n.value AND bst?(n.right) is true else if n has two children, then result is…

On S = f2; 4; 6; 10; 12; 20; 30; 60g we work with the divisibility relation R:xRy , x divides y:(i) Draw the Hasse diagram of R.(ii) Find all R-minimal elements.(iii) Find all R-maximal elements.(iv) Find all non-empty subsets U  S, so that 6 is an R-lowerbound of U.(v) Let A = f6; 10; 12g. If A admits an R-supremum,  nd it. If A admits an R-in mum,  nd it.(vi) Is R a lattice?

9. Limitation Question. Using the idea of Pumping Lemma, please explain, why we can't build a Finite Automaton to generate all and only strings of the form 1³n0n where n>=0.