You can use .every() method:
let arr1 = [false, true, true],
arr2 = [true, true, true];
let checker = arr => arr.every(v => v === true);
console.log(checker(arr1));
console.log(checker(arr2));
As mentioned by @Pointy, you can simply pass Boolean as callback to every():
let arr1 = [false, true, true],
arr2 = [true, true, true];
let checker = arr => arr.every(Boolean);
console.log(checker(arr1));
console.log(checker(arr2));