Question 6
Given positive numbers $a$, $b$, $c$, $d$ prove that at least one of the inequalities does not hold:
$a + b \lt c + d$ ;
$(a + b)(c + d) \lt ab + cd$ ;
$(a + b)cd \lt ab(c + d)$ .
$a + b \lt c + d$ ;
$(a + b)(c + d) \lt ab + cd$ ;
$(a + b)cd \lt ab(c + d)$ .