I want to control three LED with three push buttons using and or.

The logical and operator in C is '&&' not 'and'

Also, unless you have external pullup resistors connected to your buttons, you want to declare them as INPUT_PULLUP, not INPUT.

//Initialize Variables

const int ledPin = 5;       // choose the pin for the LED
const int ledPin2 = 6;
const int ledPin3 = 7;
const int inPin = 2;        // pin for button 1
const int inPin2 = 3;      // pin for button 2
const int inPin3 = 4;      // pin for button 3

void setup()

{
  Serial.begin(9600);

  pinMode(ledPin, OUTPUT);  // declare LED as output
  pinMode(inPin, INPUT_PULLUP);    // declare pushbutton as input
  pinMode(ledPin2, OUTPUT);  // declare LED as output
  pinMode(inPin2, INPUT_PULLUP);    // declare pushbutton as input
  pinMode(ledPin3, OUTPUT);  // declare LED as output
  pinMode(inPin3, INPUT_PULLUP);    // declare pushbutton as input
}

void loop()
{
  //Read button output

  int val1 = digitalRead(inPin);  // read input value
  int val2 = digitalRead(inPin2);  // read input value
  int val3 = digitalRead(inPin3);

  if (val1 == HIGH)
  { // check if the input is HIGH (button released)
    digitalWrite(ledPin, LOW);  // turn LED OFF
  } else
  {
    digitalWrite(ledPin, HIGH);  // turn LED ON
  }

  if (val2 == HIGH)
  { // check if the input is HIGH (button released)
    digitalWrite(ledPin2, LOW);  // turn LED OFF
  } else
  {
    digitalWrite(ledPin2, HIGH);  // turn LED ON
  }

  // read input value
  if (val3 == HIGH && val1 == HIGH)
  { // check if the input is HIGH (button released)
    digitalWrite(ledPin3, LOW); // turn LED OFF
  }
  else
  {
    digitalWrite(ledPin2, HIGH);// turn LED ON
    digitalWrite(ledPin, HIGH);
  }
}