tmua None Q15

tmua · Uk · specimen_paper2 Inequalities Identify Always-True Inequality from Options
15. For any real numbers $a , b$, and $c$ where $a \geq b$, consider these three statements:
$$\begin{array} { l l } 1 & - b \geq - a \\ 2 & a ^ { 2 } + b ^ { 2 } \geq 2 a b \\ 3 & a c \geq b c \end{array}$$
Which of the statements 1,2 , and 3 must be true?
A none
B 1 only
C 2 only
D 3 only
E 1 and 2 only F 1 and 3 only G 2 and 3 only H 1,2 and 3
15. For any real numbers $a , b$, and $c$ where $a \geq b$, consider these three statements:

$$\begin{array} { l l } 
1 & - b \geq - a \\
2 & a ^ { 2 } + b ^ { 2 } \geq 2 a b \\
3 & a c \geq b c
\end{array}$$

Which of the statements 1,2 , and 3 must be true?\\
A none\\
B 1 only\\
C 2 only\\
D 3 only\\
E 1 and 2 only\\
F 1 and 3 only\\
G 2 and 3 only\\
H 1,2 and 3\\