Question

The diagram rerpesents responses to a survey that include statements p and q . Which statement is true?

Answer 1

c.The number of responses for which
`p\wedge q` is 46.

Explanation:

We are given that a diagram represents responses to a survey that includes statements p and q.

We have to find which statement is true in the given option.

From given diagram

`p\wedge q=46`

`p/q=0`

`(p\vee q)'=20`

Option A is false because
`p\wedge q=46`.

`p-q=p-p\wedge q=p-46`

`0=p-46`

`p=46`

`p\vee q=p+q-p\wedge q`

`p\vee q=46+46-46=46`

Because q=46

Hence, option c is true .

Answer:c.The number of responses for which
`p\wedge q` is 46.

Answer 2

C. The number of responces
`p\vee q` is also 46

Explanation:

Note that:

• 
  `p\wedge q` means both p and q must hold;
• 
  `p\vee q` means either p or q must hold.

From the diagram,

• the number of responses
  `p\wedge q` is 46;
• the number of responces
  `p\vee q` is also 46;
• the number of responces
  `p\setminus q` is 0;
• the number of responces which are neuther p nor q is 20.

So, you can state that the correct answer is C