Subsets

Let [n] = {1,2,3,....,n}. We divide [n] into m subsets A1,A2.....Am, such that they satisfy the properties:
1). For all i, |Ai| is odd.
2). For all distinct i and j, |Ai ∩ Aj| is even.
Prove that m<=n, where for a set X, |X| denotes number of elements in X.

Courtesy : Prof. Sundar Vishwanathan, IIT Bombay