The statement `pvec(qvecp)` is equivalent to (1) `pvec(pvecq)` (2) `pvec(pvvq)` (3) `pvec(p^^q)` (4) `pvec(pharrq)`

The logical statement [~(~pvvq)vv(p^^r)]^^(~q^^r) is equivalent to (a) (~p^^~q)^^r (b) ~p vv r (c) (p^^r)^^~q (d) (p^^~q)vvr

The Boolean Expression (p^^~ q)vvqvv(~ p^^q) is equivalent to : (1) ~ p^^q (2) p^^q (3) pvvq (4) pvv~ q

The Boolean expression sim(p vv q)vv(sim p^^q) is equivalent to (1)-p(2)p(3)q(4)sim q

The statement ~(pharr~ q) is (1) equivalent to pharrq (2) equivalent to ~ pharrq (3) a tautology (4) a fallacy

Using truth tables, prove the following equivalences : (1) ~pvvq-=~(p^^q)to[~pvv(~pvvq)] (2) p""iffq-=(p^^q)vv(~p^^~q) (3) (p^^q)tor-=pto(qtor)

If the statement p and q are true and the statements r and s are false, fing the truth values of : (1) (~pvvq)to(s^^~r) (2) [p^^(q^^r)]vv[(pvvq)^^(~rvvs)] (3) ~[(~p^^r)vv(sto~q)]iff(p^^r) .

If vec a is perpendicular to vec b and vec r is non-zero vector such that pvec r+(vec r*vec a)vec b=vec c then vec r=(vec c)/(p)-((vec a*vec c)vec b)/(p^(2))( b) (vec a)/(p)-((vec c*vec b)vec a)/(p^(2))(vec a)/(p)-((vec a*vec b)vec c)/(p^(2))( d) (vec c)/(p^(2))-((vec a*vec c)vec b)/(p)

Let vec(a) = hat(i) + 2hat(j) + 3hat(k) , vec(b) = 2hat(i) + hat(j) + hat(k), vec(c) = 3hat(i) + 2hat(j) + hat(k) and vec(d) = 3hat(i) - hat(j) - 2hat(k) , then . If vec(a) xx (vec(b) xx vec(c)) = pvec(a) + qvec(b) + rvec(c) , then find value of p,q are r.

Statement 1:vec a=3vec i+pvec j+3vec k and vec b=2vec i+3vec j+qvec k are parallel vectors if p=9/2 and q=2. Statement 2: if vec a=a_(1)vec i+a_(2)vec j+a_(3)vec k and vec b=b_(1)vec i+b_(2)vec j+b_(3)vec k are parallel,then (a_(1))/(b_(1))=(a_(2))/(b_(2))=(a_(3))/(b_(3)) .