Question

I being given that x denotes 'greater than' $\varphi$ denote 'equal to' > denotes 'not less than' $\perp$ denotes 'not equal to $\Delta$ denotes 'less than' and + denotes 'not greater than' choose the correct statements from the following
If a x b $\Delta$ c it follows that

• A. $a\varphi \Delta b$
• B. $b<a\times c$
• C. $a<b+c$
• D. $b<a\varphi c$

Answer 1

The correct option is C $a<b+c$

Using the usual notations we have
(1) The statement is $a>b<c\Rightarrow a=c<b$ which is false $[\because c>b]$
(2) The statement is $a>b<c\Rightarrow b<a>c$ which is false $[\because b<a]$
(3) The statement is $a>b<c\Rightarrow a<b>c$ which is true
(4) The statement is $a>b<c\Rightarrow c<b<a$ which is false$[\because b<a]$