Write the component statement of the following statement and check whether the compound statement is true or false
(i) r : All real numbers are complex and all complex numbers are real
(ii) s : All square are rectangle and all rectangle are not square
(iii) t : 2 is a root of equation `(x-2)^2=0` and 3 is a root of equation `x^2-3x=0`
(iv) Sphere is 3-D solid and square is 2- demensional figure

Explanation

(i) Component statements are
p : All real number are complex number (True)
q : All real complex number are real number (False)
Connective word is "AND" . Since all component statements are not true , so compound statement r is false
(ii) Component statmets are
p : All square are rectangle (True)
q : All rectangle are not square (True)
Here connective is "AND" and all component statement are true , so s is true
(iii) Component statement are
p :2 is root of equation `(x-2)^2=0` (True)
q : 3 is a root of equation `x^2-3x=0` (True)
Both p and q are true . so t is true
(iv) Components statement are
p : Sphere is 3-D solid (True)
q : Square is 2-dimensional figure (True)
Both p and q are true so u is true