LOGICAL REASONING

Which sentence is a statement?

• What is the meaning of factor?

• Go and brush your teeth.

• Good morning!

• The highest common factor of 21 and 28 is 7.

Which statement is false?

• Some quadratic function graphs intersect the x-axis.

• Bougainvillea is the national flower of Malaysia and Kuching is the capital of Sarawak.

• Hibiscus is the national flower of Malaysia or Rafflesia is the biggest flower in Malaysia.

• $If\ x>3,\ x>1.$

Given the implication

 $'if\ m>10,\ then\ m>8'$  , determine the false statement.

• The converse of the given implication is  $'if\ m>8,\ then\ m>10'$  
  

• The inverse of the given implication is  $'\ if\ m\le10,\ then\ m\le8'$  
  

• The contrapositive of the given implication is  $'\ if\ m\le8,\ then\ m\le10'$  
  

• The inverse of the given implication is  $'if\ m\ge10,\ then\ m\ge8'$  
  

Which of the following implications is false?

• $If\ p-5<0,\ then\ p-7<0$

• $If\ ab=0,\ then\ a=0\ or\ b=0\ or\ a=b=0.$

• $If\ 3a>b,\ then\ a>b.$

• $If\ \theta=45\degree,\ then\ \sin\ \theta=\cos\theta.$

Which of the following statement is true?
I Some quadratic equations have two roots.
II $0.25\times10^4$  is a number in standard form.

III  $\phi\ is\ a\ subset\ of\ M\cap N.$  

• I only
  

• I and II only
  

• I and III only
  

• II and III only
  

Choose the correct statement.

• $3^2=9\ or\ 5<4.$

• $5^2-1^2=4^2\ or\ 3^2-2^2=4$

• Some of the complete squares are odd numbers.
  

• $5^2-3^2=4^2\ and\ 2^2-1^2=1^2$

If p and q both false statements respectively, then

• not p and not q is a true statement.

• p and q is a true statement.

• not p and q is a true statement.

• not p or q is a false statement.

Which of the following are statements?
I   $a+b=5$ 

II  $4>6$ 

III  $a\left(a+2\right)=a^2+2a.$  

• I and II only
  

• I and III only
  

• II and III only
  

• I, II and III only
  

Which of the following implications is true?

• If $M\cap N=\ \left\{\ \ \ \right\},\$ then $M=\ \left\{\ \ \ \right\}$
  

• If $a>-3,\$ then $a^2>9$ .
  

• If $a<0$ , then $a^2<0$
  

• If $n=-2$ , then $n^2+2n=0$
  

Which of the following statements is true?

• $B\subset B$ and $\phi\ \subset\ B$
  

• $2\ \in\ \left\{\ \ \right\}$ and $3\ \in\ \left\{2,3\right\}$
  

• $m\times m=2m$ or $2\times\frac{1}{3}=2\frac{1}{3}$
  

• $2x+1=2\left(x+1\right)$ or $\frac{2x+5}{2}=x+5$