Show that `(p vee q) rarr r-= (p rarr r) wedge (q rarr r)`

Show that the vee: R xx R rarr R given by (a, b) rarr max {a, b} and the * : R xx R rarr R given by (a, b) rarr min {a , b} are binary operations.

Show that * : R xx R rarr R is given by (a, b) rarr(a+4 b)^2 is a binary operation.

Show that +: R xx R rarr R and xx: R xx R rarr R are commutative binary operaions, but - : R xx R rarr R and -:: R_* xx R_* rarr R_* are not commutative.

Let P be the set of all subsets of a given set X. Show that uu: P xx P rarr P given by (A, B) rarr A uu B and nn: P xx P rarr P given by (A, B) rarr A nn B are binary operations on the set P .

(p wedge ~q) wedge (~p wedge q) is

Identify the false statement a) ~[p vee (~ q)]-=(~p)wedge q b) [ p vee q)] vee (~p) is a tautology c) [p vee q)] vee (~p) is a contradiction d) ~ [pwedge (~p)] is a tautology

If p and q are two statements, then (p rArr q) hArr (~q rArr ~p) is a

Show that * : R xx R rarr R given by a * b= a+2 b is not associative.

Show that * : R xx R rarr R defined by a * b =a+2 b is not commutative.